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L161— O-1096 


DETAILED FACTORS IN 
LATIN PROGNOSIS 


BY?) 
ORLIE M. CLEM, Pu.D. 


ASSOCIATE PROFESSOR OF EDUCATION 
YPSILANTI STATE NORMAL COLLEGE 


TEACHERS COLLEGE, COLUMBIA UNIVERSITY 
CONTRIBUTIONS TO Epucation, No. 144 


Published by 
Teachers College, Columbia Cnibersity 
New York City 
1924 


pyrig 


Co 


ht, 1924, by Ortiz M. Crem 


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DIET RL 


SO eo 


ACKNOWLEDGMENTS 


A stupy of this character can be carried on only through the 
sympathetic codperation of many persons. I am indebted chiefly 
to Professor Thomas H. Briggs under whose keen insight and 
kindly guidance the study has been made. His careful and pains- 
taking criticisms were always a source of helpfulness and encour- 
agement. My thanks are due to Professors Rudolph Pintner and 
Gonzalez Lodge for many valuable aids and suggestions. Special 


- gratitude is felt towards Dr. Herbert Anderson Toops, of the 


Bureau of Educational Research of Teachers College. His advice 
and direction in statistical technique have been invaluable. My 
thanks are due to Mrs. Zaida Minor, also of the Bureau of Educa- 
tional Research, for her untiring statistical assistance. 

Space will not permit an individual acknowledgment of gratitude 
to all teachers and pupils who participated in the study. The 
heads of the classical departments at each school, Miss Elizabeth 
Nammack at Wadleigh, Mr. Michael Solomon at De Witt Clinton 
High School, New York City, and"Dr. Ernest Riess at Boys’ High 
School, Brooklyn, have my sincere appreciation for their full 
codperation and many kindnesses. It was they who made the 
study possible. 

O. M. C. 


5920257 


iil 


Le 


Vs 


VII. 


CONTENTS 


PAGE 

. BRIEF SURVEY OF PREvViIousS STUDIES. . ... . 1 
PEE EL ROBLES re ae eee eral When ee, So hh OS 
Data . 4 
1. Plan of the Eenerinent UE ek ie er a 

2. Subjects . . Saat ee tn ee A 

3. Factors Goniderd ‘ot Each Pupils BN eae ae 
AEE CMlerione tare a ee eee aa 1S 
STATISTICAL TREATMENT OF DaTA. ... 2a 
1. Tabulation and Transmutation of Raw fect, aa Es 

2. Raw Coefficients of Correlation SAREE Tt Wo ee Be) 

3. Significance of Raw Correlations .. 21 


4. Effect of Detailed Factors as Shown by Multiple 
Ratio Correlation Coefficients, and Selection of 


ETORNOSISSLACLOTS* rin ee Meme st orate, 2G 
PPL RACTICAT IMPLICATIONS | oe en ee a RS) CAD 
OUMMARIZED CONCLUSIONS 44-0 . 8. ek tS ee 4D 


ACEP ENT Nae en eet aan eee oe. ae) A OL 


DETAILED FACTORS IN LATIN 
PROGNOSIS 


CHAPTER I 
BRIEF SURVEY OF PREVIOUS STUDIES 


To reduce misdirected effort is the first aim of any study in 
educational prognosis. Tbe method, if it is to be other than spec- 
ulative, requires an analysis of the factors which have made for 
success In a given situation with a view to determining the probable 
effect of the same factors in a second situation. Assuming that 
specific abilities are required in different types of learning, the 
problem of the investigator is to devise means for segregating and 
measuring these specific abilities, as a basis of prognosis. Previous 
to this study, four investigations have been made in the field of 
prognosis. 

In 1914, Dr. Truman Lee Kelley! investigated the relative 
predictive value of elementary school marks, teachers’ estimates, 
and some special tests upon the success of pupils in mathematics, 
history, and English, in the first year of the high school. Apply- 
ing the regression equation for the first time to educational meas- 
urement, Kelley found the individual and combined prognostic 
values of: 


1. A pupil’s average in Grades 4-7. 

2. The teacher’s estimate of a pupil on four traits: intellec- 
tual ability, conscientiousness, emotional interest, and 
oral expression. 

3. The scores of pupils on some special tests in school subjects. 


Kelley’s results showed that these instruments of prognosis should 
be ranked in order of importance as listed above. 

Dr. Agnes Low Rogers,” in 1918, developed a group of six tests 
for predicting ability in mathematics. She ascertained that 

1 Kelley, Truman Lee: Educational Guidance. Teachers College, Columbia 
University, Contributions to Education, No. 71. New York, 1914. 

2 Rogers, Agnes Low: Experimental Tests of Mathematical Ability and Their 


Prognostic Value. Teachers College Contributions to Education, No. 89. New 
York, 1918. 


1 


2 Detailed Factors in Latin Prognosis 


mathematical ability was not a general trait, but was made up of 
a series of loosely connected capacities; that consequently no single 
test was an index to mathematical ability. Algebraic, geometric, 
and verbal abilities seemed to be of equal significance in math- 
ematical ability. 

Dr. Elbert Kirtley Fretwell,! in 1918, used as a basis of prognosis 
a group of standardized tests. He found that “academic success in 
the first year of the junior high school could be predicted more 
successfully by a group of standardized educational tests than by 
either elementary school marks, or teachers’ estimates, or age.” 

In 1921-22, Dr. William Sims Allen? conducted an investigation 
entitled A Study in Latin Prognosis. Dr. Allen, at the beginning 
of the first semester, 1921-22, gave twenty-one psychological tests 
to three hundred sixty-four boys taking first year Latin in the 
Boys’ High School, Brooklyn. At the end of the semester he gave 
to the same pupils eleven pairs of Latin tests devised by Professor 
Thomas H. Briggs. These tests were constructed so that they 
could be objectively scored and covered the eleven types of work 
done in the first semester of Latin. Dr. Allen, through multiple 
correlation procedure, chose from the twenty-one psychological 
tests a prognosis battery of six tests which gave the highest corre- 
lation with the eleven Latin tests used as criterion. These six 
tests: Briggs Analogies Tests Alpha and Beta, Thorndike Word 
Knowledge Tests A and B, Rogers Interpolation Tests 1 and 2, 
when combined gave a multiple correlation coefficient of .588. 
They also predicted ability as well in mathematics and English as 
in Latin. 

1 Fretwell, Elbert Kirtley: A Study in Educational Prognosis. Teachers College 
Contributions to Education, No. 99. New York, 1919. 


2 Allen, William Sims: A Study in Latin Prognosis. Teachers College Contribu- 
tions to Education, No. 135. New York, 1923. 


YU, 


CHAPTER II 


THE PROBLEM 


x THE purpose of this study is to find the effect of certain detailed 
factors upon a pupil’s success in first year Latin, to choose the 
most effective factors, and through multiple correlation to obtain 
their combined effect as a basis for prognosis. 

Dr. Allen used one factor as a basis for prognosis,—psychological 
tests. The aim of the present study is to find the influence of 
many possible factors, including those measured by the Allen 
Battery of six tests. The original analysis of the problem was, 
made on the basis of, “What are the possible factors which in- 
fluence a pupil’s success in first year Latin?” Obviously the 
original list was incomplete because no one can bottle up all the 
human influences affecting a pupil’s Latin product. | However, the 
original list was greatly abbreviated. Some factors were elim- 
inated because they appeared too subtle and elusive for our present 
scales of measurement; others because data could not be secured, 
or if at all only with too great difficulty; others because they would 
not lend themselves to statistical treatment. Of the factors re- 
tained, it was not presumed at the outset that each had equal 
reliability when taken at its face value. For example, the age of a 
pupil is an objective measure which should be accurate. But 
“the average number of minutes daily”? which a pupil says he 
spends in the preparation of Latin is a different kind of measure. 
Some pupils may have little ability in estimation. Some will by 
nature estimate too high and others too low where they themselves 
are concerned. Honesty with self may be an important factor. 
Practically every degree of reliability is represented by the various 
factors as shown by the correlations in the three schools studied. 


One of the important aims of this study is to find to what degree 


the various factors are reliable for different groups. 
| The purposes of this investigation then are: 


_ 1. To find in the groups studied the empirical effect of ee 


detailed factors on success in first year Latin, regardless of what 
their reliability may subjectively appear to be. 
2. To build up a battery of factors as a basis for prognosis, 


" 


having consideration for the availability and objectivity of data. | 
3 = 


CHAPTER III 
DATA 


1. PLAN OF THE EXPERIMENT 


Tus study supplements the one made by Dr. William Sims 
Allen, 1921-22, in the Boys’ High School, Brooklyn, entitled A 
Study in Latin Prognosis. It was arranged for by the department 
of secondary education of Teachers College in codperation with 
the classical departments of three schools of New York City: Boys’ 
High School, Brooklyn; Wadleigh High School; De Witt Clinton 
High School. 


2. SUBJECTS | 
\ Phe subjects for this experiment consist of three groups: 


Group 1. Two hundred fifteen boys in the Boys’ High School, 
Brooklyn, who had elected to study Latin. They were the ones 
still remaining in school of the three hundred sixty-four used by 
Dr. Allen in his experiment. Dr. Allen notes that the original 
three hundred sixty-four were grouped in eleven classes, the groups 
having been made according to the pupils’ scores in the Otis group 
test of mental ability; they were taught by four teachers. No boy 
had previously studied Latin. The average age was thirteen and 
one half years. 

Group 2. Ejghty-eight first year girls of the Wadleigh High 
School, New York City. Of the eighty-eight who took the prog- 
nosis tests at the beginning of the semester, eighty remained in 
school and took the Latin tests at the end of the semester. This 
study deals with the eighty pupils. The girls were grouped in 
Latin classes at Wadleigh according to the Terman group test of 
mental ability. From the Latin classes in the school, one class 
was chosen at the lower, one at the middle, and one at the upper 
range of ability. The average age was slightly less than fourteen 
years. 

Group 3. One hundred ten first year boys of the De Witt Clin- 
ton High School, New York City. Of the one hundred ten who 
took the prognosis tests at the beginning of the semester, one hun- 
dred three remained in school and took the Latin tests at the end 

¢ 


Data 5 


of the semester. This study deals with one hundred three pupils. 
They were sectioned according to the Otis group test of mental 
ability, and the three classes used in this study were selected on 
the same basis as at Wadleigh. The average age was slightly more 
than fourteen years. — ) 


8. Factors CONSIDERED FoR EAcH Pupin 


Approximately sixty separate items were considered for the three 
groups. They have been classified under sixteen heads called 
throughout this study, “Factors.’’ Factors V, VI, and VIII were 
omitted from Group 1 for reasons explained later. 


Factor I. Scores Made in Each Test of the Allen Prognosis 
Battery. 


The tests are: 


1. Briggs Analogies Test Alpha.? 

. Briggs Analogies Test Beta.’ 

. Thorndike Test of Word Knowledge A. 
. Thorndike Test of Word Knowledge B.° 
. Rogers Interpolation Test 1.4 

. Rogers Interpolation Test 2.4 


> Or em OO rw 


A brief description of these tests follows: 


Briggs Analogies Tests Alpha and Beta consist of 72 items. 
They measure knowledge of form and ability to see relationship 
between words. 

Thorndike Tests of Word Knowledge A and B consist of 100 
items each. They measure the ability to recognize the meaning 
of words. 

Rogers Interpolation Tests 1 and 2 consist of 107 items each. 
They measure the ability to interpolate numbers, that is, to supply 
omissions in a series of varied arithmetical progressions. 

For the first group of pupils (215 boys, Boys’ High School, Brook- 


1 For a more complete description of these tests see: Allen, A Study in Latin 
Prognosis, p. 4. 3 

2 Copies of the Briggs Analogies Test may be secured from Professor Thomas H. 
Briggs, Teachers College, Columbia University. 

3 Copies of Thorndike Word Knowledge Tests may be secured from the Bureau 
of Publications, Teachers College, Columbia University. 

4 Copies of Rogers Interpolation Test may be secured from the Bureau of Pub- 
lications, Teachers College, Columbia University. 


6 Detailed Factors in Latin Prognosis 


lyn) the scores secured by Dr. Allen in these tests were used. The 
tests were scored by fifteen teachers of Boys’ High School and 
checked by Dr. Allen. 

The second group of pupils (80 girls, Wadleigh High School) 
were given the above tests by the writer at the opening of school, 
September, 1922. The papers were scored by three Latin teachers 
and checked by the writer. 

The third group of pupils (103 boys, De Witt Clinton) were given 
the tests by the writer at the opening of school, September, 1922. 
In this group the three classes were taught by the same teacher. 
The papers were scored by this teacher and checked by the writer. 


Factor II. Intelligence Quotient. 

For the first and third groups the Otis group test of mental 
ability was used, and for the second, the Terman. Strictly speak- 
ing, the term I. Q. should apply only to the Binet-Simon scale. 
But the administration of the Binet-Simon scale to such a large 
group in an experiment of this character is impossible. Hence, in 
school administration the term I. Q. has come into rather common 
acceptance in dealing with groups of pupils measured by either of 
the above tests. Each test is accompanied by a table for the 
transmutation of raw scores into approximate I. Q.’s. It is not 
claimed that they are as accurate as the I. Q. of the Stanford 
Revision of the Binet-Simon Test. 


Factor III. Age. 


The age was secured at the beginning of the semester. The 
time it was taken, however, would in no way affect the correlations 
inasmuch as we may add, subtract, divide, or multiply a series of 
scores by the same constant without affecting the correlation. 


Factor IV. High School Attendance. 


The number of days attendance during the semester was used. 


Factor V. Elementary Attendance. 


The number of days attendance during the last year of the 
elementary school was used. This factor is lacking for Group 1. 


Factor VI. Elementary School Marks for the Last Year, in All 
Subjects. 


The promotion marks of both the teacher and the principal were 
used for the following fifteen items: 


Data 7 


1. Reading 9. Geography 

2. Grammar 10. Music 

3. Composition 11. Drawing 

4, Spelling 12. Cooking (Science for Group 3) 
5. Penmanship 13. Sewing (Shop for Group 3) 

6. Arithmetic 14, Physical training 

7. Arithmetic 15. General estimate 

8. History and civics 


No elementary school marks were obtainable for Group 1. Pro- 
motion cards are destroyed after a year at the Boys’ High School, 
and no duplicates are kept at many of the elementary schools. 


Factor VII. High School Marks in All Subjects. 
The semester mark for each pupil was secured in the following 
subjects: 


Group 1 Group 2 Group 3 
Latin Latin Latin 
English English English 
Mathematics Biology Biology 
Drawing . Civics Mathematics 
Music Drawing Civics 
Physica] training Music Drawing 
Physical training Music 
Physical training 
Elocution 


Facror VIII. Ranking of Pupils by Teachers on the Following 
Twelve Traits: 


b—_ 


. Perseverance 

. Industry 

. Earnestness 

. Nerve stability 

. Orderliness 

. Self-confidence 

. Accuracy 

. Right attitude toward criticism 

. Frequency in securing help from teacher 
. Promptness and regularity in doing work 
. Ability to work independently 

. Desirable social and moral attitudes 


Oo COs SD Or & OC WO 


tet et 
© = © 


No rankings were secured of the pupils in Group 1. Because of 
the possible changes in administration and instructional force, and 
also the lapse of time, it was thought that a ranking made after a 
year would be impracticable. To the teachers of Groups 2 and 3 
the following blank was given: 


Detailed Factors in Latin Prognosis 


RANKING OF PUPILS BY TEACHERS 


Each teacher will please rank his or her pupils on the following points. 


ing them use this method: 


In rank- 


1. Give those in the highest 10 per cent of the class a rank of 1. 


2. Give the next 20 per cent a rank of 2. 
3. Give the next 40 per cent a rank of 3. 
4. Give the next 20 per cent a rank of 4. 
5. Give the next 10 per cent a rank of 5. 


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wanorors [TTP TPEPEPE EEE ELLE 
Seem SA AUBEUEURAUEUORUSENEUEGRELGBUEEAELAER 


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HRSA SHHASHRHAHNHSCrNOAS 
2 ned pe et et et CN 


NAMES OF PUPILS 


ScHOOL 
TEACHER 
SECTION 


Data 9 


(it will be noted from the above blank that each teacher was 
asked to rank his or her pupils on the twelve traits by dividing 
them into five groups. Those in the upper 10 per cent were to be 
given a rank of 1, those in the next 20 per cent a rank of 2, those 
in the next 40 per cent a rank of 3, those in the next 20 per cent 
a rank of 4, and those in the lowest 10 per cent a rank of 5. It was 
thought that this method was just as accurate and not nearly so 
laborious as ranking each pupil in a position relative to every other. | 

The following set of directions was also given to each teacher. 
No particular merit is claimed for these directions. The ranking 
would possibly have been just as reliable without them. To at- 
tempt to define perseverance by the use of other words is difficult; 
and so it is with many of the other traits. 


DIRECTIONS FOR RANKING PUPILS 


Each teacher in ranking pupils will please consider the following interpretations: 
PERSEVERANCE: 
Ability and tendency of pupil to keep at, to continue, whatever work under- 
taken, regardless of difficulty or unpleasantness. 
INDUSTRY: 
Attention to work at hand. Pupil is alert and active in taking up new tasks 
and in carrying them through. 
EARNESTNESS: 
Pupil is serious and intent in his work; he is purposeful, determined, and eager. 
NERVE STABILITY: 
Nerve condition of pupil is stable and balanced. There are no disorders which 
harass or handicap him in his work. 
ORDERLINESS: 
Pupil is neat and orderly in his work. 
SELF-CONFIDENCE: 
The pupil believes in self, has faith in his own ability to do things. 
ACCURACY: 
Painstaking, careful in work; has details correct. 
Riegut ATTITUDE TOWARD CRITICISM: 
Takes criticism without resentment and attempts to remedy faults. 
PROMPTNESS AND ReauLarity In Dorne Work: 
Does work at the time required, and regularly. 
FREQUENCY IN SEcuRING HELP rromM TEACHER: 
Rank on number of times pupil secures help, or the amount. Do not consider 
the effectiveness of the help in this ranking. 
Asinity TO Work INDEPENDENTLY: 
Pupil shows initiative and originality, power to proceed alone without help 
from teacher or another. 


10 Detailed Factors in Latin Prognosis 


DESIRABLE SoctAL AND Mora ATTITUDES: 
Habits and manners of pupil are such that he gets on well with his fellows and 
has a wholesome influence among them. 


Factor IX. Study and Conditions for Study. 


1. Amount of outside help on Latin and by whom given. 
2. Attendance at movies. 
3. Amount and character of daily sleep. 


Factors IX to XVI were secured from pupils near the close of 
the semester by means of the questionnaire which follows: 


QUESTIONNAIRE USED FOR SECURING FACTORS IX TO XVI 


Name of Pupil eis c.¢- es ba 
Last, First, Middle Initial 


Address of Pupil soc35 0 fu fea Oe < oe ee 


I. Stupy AND CONDITIONS FOR STUDY 


If father write “father”; if brother, write ‘‘brother,”’ etc.) 


8. If you do receive help, what is the average number of minutes daily?......... 
(Number of minutes) 


4, Estimate the number of times you go to the movies each week.............. 


5. What is the average number of hours that you sleep daily?.................. 
(Give to nearest hour) 


6. Do you sleep about the same number of hours each night?.................- 
(Answer yes or no) 


II. InpIvipvuAL INTERESTS AND AMBITIONS 
1. Do you plan to attend high school next year?.................0ccccecevces 


2. Do you plan‘to graduate from high school... .J.1.5s) +25 > o+s one ee 
(Answer yes or no) 


8. After high school, what do you expect to do? You will show this by placing a 
check before one of the following. If you are not quite sure, check the answer 
which seems more nearly correct. 

1. To attend college 

. To attend teacher-training or normal school 

. To go to trade school 

. To go to some special] school 

. To work at home 

. To go to work away from home 


aS Or & 09 


Data if 


4. As your life work, what are you planning for? Place a check before one of the 
following. If you are not quite sure, check the one which seems more nearly 
correct. 

1. Business 3. Profession 
2. Trade 4. Home 
III. Oursipr Worx 


1. Do you take music lessons outside of school? 


© © 0; 0 Bio 0 oe 6 66) .6 6 8 0 be 8 6 6 6 8S et se 8 6 


eee eer DEPOT OUTS Weel Vr 17. Fee oleate td hed ast Ge One bio Paes s ove dae 
(Give number) 

3. Do you study any language or any school subject outside of school?.......... 
(Answer yes or no) 

eR WORLD Ole gato nic cue sos Average number of hours weekly?............... 


(Give number) 

SO you work outside of school'for’your parents? eo. cleis ie ene a diene 6 cs oretele 
(Answer yes or no) 
6. If so, what is the average number of hours that you work for them weekly?...... 
(Answer to nearest hour) 


(Answer yes or no) 


A. If you do work for others besides your parents, what average number of 


(Give to nearest hour) 


B. Name or kind of work which you do for those who are not your parents... . 


C. How much money do you receive per week on the average for this work? 


eee eee ee ee ee ee ee es eee sense ee ese ee ee ee ere ee ese seers os eee ees ee ee eevee 


(Dollars) (Cents) 


IV. Srupy, AND Ranxincs or Pupits 


(1) (2) (3) (4) (5) 
Names of Study Importance Preference Preference 
Subjects at Home of Subject for Subject for Teacher 


|S | | —  ———————_—— |) 
FESS 
| 
—————— | LN es 
ee | | ee | — | 


_S— | SSSSSFSSFSSsE SEE 


12 Detailed Factors in Latin Prognosis 


V. Exrra-Curricuuar ACTIVITIES 
Go down the following list. Check once those activities in which you have par- 
ticipated. Check twice those activities in which you have held an office, during 
the semester. 


1. General Organization 12. Dramatic Club 23. Court 
2. Athletic Association 13. Debating Club 24. Assembly 
3. Hockey 14, Literary Society 25. Class Officer 
4. Basket-ball 15. Poetry Club 26. Official Section Officer 
5. Foot-ball 16. Bank 27. Roosevelt Memorial 
6. Swimming 17. Newspaper Association 
7. Track 18. Magazine 28. Red Cross 
8. Tennis 19. Handbook 29. Library 
9. Orchestra 20. Curricula Club 30. Honor Roll 
10. Glee Club 21. Lunch 31. Boy Scouts 
11. Band 22. Fire Drill 32. Camp Fire Girls 
33. Hi Y. 


The writer, in giving the questionnaire to the pupils, explained 
for their protection that no teacher would be in the room during 
the time it was given, that the answers would be treated as con- 
fidential, and that the pupils should write what they actually 
believed. It is the opinion of the writer that they did this to a 
very great degree. 


Factor X. Individual Interests and Ambitions. 
The following data were secured: 
1. Plan for the following year. 
2. Does the pupil plan to graduate? 
3. Plan after graduation. 
4. Plan for life work. 


Factor XI. Outside Work. 
The following data were secured: 

1. Amount of time given to music lessons. 

2. Amount of time given to the study of any language or any 
school subject outside of school. It was explained here that 
the question meant any language or any school subject which 
the pupil was not then studying in school. 

3. Amount of time given to work for parents outside of school. 

4. Amount and kind of work done for persons besides parents with 
amount of money received. 


Factor XII. Amount of Home Study. 
Factors XII to XV were secured by means of the rectangular 
chart on the questionnaire. The pupils of the three schools 


Data 13 


studied the same subjects in each respective school. The names 
of these subjects were written on the blackboard, and each pupil 
copied the list into column (1) of the chart. In column (2) he 
wrote opposite each subject the average amount of time spent 
daily on study at home. The pupils in each of the schools did no 
study at school, inasmuch as the schools operate on the double 
session basis. 


Factor XIII. Importance of Subject. 

Each pupil was asked to rank in column (3) the subjects listed 
in column (1) in “what he considered their order of importance 
to him.” ‘The most important was to be given a rank of 1, the 
next important 2, and so on. 


Factor XIV. Preference of Pupil for Subject. 

Using the same method as above, each pupil was asked to rank 
in column (4) the subjects as he liked them, regardless of their 
importance or any other consideration. 


Factor XV. Preference of Pupil for Teacher. 
Using the same method as above, each pupil was asked to rank 
in column (5) the teachers of the various subjects as he liked them. 


Factor XVI. Participation of Pupil in Extra-Curricular Activi- 
ties. 

From a study of the extra-curricular activities of the three 
schools, an inclusive list was made of all those of any importance 
to which freshmen were eligible. The pupil was asked to check 
once those activities in which he had participated, twice those in 
which he had held an office, during the semester. 


4, Tur CRITERION 


[iy he criterion used in this experiment was a group of Latin tests 
given at the end of the semester... For Group 1, the results of Dr. 
Allen’s experiment were used. He gave eleven Latin tests devised 
by Professor Thomas H. Briggs. One test was given to each of the 
following fields:é 2 2 3 — 


1. Nouns 

2. Vocabulary 
3. Construction 
4, Derivation 


1 For a more complete description of these tests, see: Allen, A Study in Latin 
Prognosis, p. 9. 


14 Detailed Factors in Latin Prognosis 


5. Syllabification 

6. Gender 

7. Pronouns 

8. Conjugation 

9. Pronunciation 

0. Translation from English to Latin 
1. Translation from Latin to English 


pt ee 


<. Each test was constructed so that it could be scored in objective 
units, so easy that the poorest pupil could make some score, and 
so difficult that the best pupil could not make a perfect score. The 
methods of scoring, timing, and administration were similar to 
those of any good standardized test. 

For Groups 2 and 8 a series of ten tests, devised by the writer 
and paralleling those of Professor Briggs, was given. The pro- 
noun test was omitted inasmuch as the subject had not been 
covered in the two texts used. Only one set of tests was given to 
Groups 2 and 3 owing to the high reliability of the two forms. 
These tests covered the materials in the texts of the two schools. 

(_In order that all pupils might more adequately be measured, the 
tests included only materials studied by the poorest section. It 
may readily be claimed that this penalizes the brightest section; 
yet the plan seems more desirable than to test the poorest section 
on materials they have never studied. 

- For Groups 1 the Latin tests were Stored by the Latin teachers 
of Boys’ High School, Brooklyn, and checked by Dr. Allen. For 
Groups 2 and 8 the papers were scored by the Latin teachers of 
Wadleigh and De Witt Clinton High Schools and checked by the 


writer. 


CHAPTER IV 
STATISTICAL TREATMENT 


1. TABULATION AND TRANSMUTATION OF Raw ScorRES 


The Criterion. For each of the three groups a combined weighted 
criterion score was computed for each pupil in the following 
manner: 

In Dr. Allen’s experiment, thirteen Latin teachers weighted the 
eleven tests... The median of their weightings is shown in Table I. 


TABLE I 


Wericuts Given THE LaTIN CRITERION TEsts BY THIRTEEN 
Latin TEACHERS 


Test Weight 
NOUNS ea Cane state ade ial ee on tae Bea ea cB fc ope sha es 9 
OV ONSITE re ee pete etree eed aes I ees a ah 10 
OTISLEUCLIOLU Me ae Se Rats te ove ate ere Ramla wired vas 11 
DCrIVAL itt etre tee se fate eine toe ae Ce OG ee wierd a ace 6 
IMLS DIN CALIGNin eet orc kee ett pie sea tr Pe ts oleae baa cos 5 
CPST irr teeny Shee eee eet) eee ee ae oe dag sy Sieg wisi wd 5 
PE POUULS Pompey rt eel eee ots, CEE hc chlo eos “av Giale 9 
Ce aTEA Te ASOT is Gre 8 a RON let Wie ef ON WR ee a Er 16 
eer OAC LAE LON eee ere ene ne ane he ante b's vin eines 4 
ransigtion trom bnghisit tOnLAtyy ys. ccs. fos ete se alee 2 ease 12 
Prasislation (ont LAtinitO LNClISl.. | oc: doe oeee sence ase 13 


In weighting any series of tests for purposes of statistical com- 
putation, it is necessary to take account of the standard deviations 
of each test. Hence, the weighted score in any test is equal to 
the actual score divided by the standard deviation, times the weight 
assigned. ‘The combined weighted criterion score of any pupil in 
all the tests is the sum of the weighted scores. 

ae 

S =the combined weighted criterion score desired for each pupil. 

B, B, Bs . . . By=the weights assigned each test in the 
above table. 

X1, Xo, X3 . . . Ai=the raw scores made by a pupil in 
each test. 


1 Allen, A Study in Latin Prognosis, p. 19. 
15 


16 Detailed Factors in Latin Prognosis 


Then, the formula becomes: 


XxX. XxX. 
S=B,—=+B, + ousie NPs +By — 


O71 02 O11 


The formula at first sight appears laborious, but in actual practice 
becomes rather simple. 


By, Bo SO). SB and: ‘ow og, eres to are constant. 
each test. Hence, we may write the formula: 
B B B 
s=— X,4+—X.+ Oe eS += Xu 
01 02 O11 
il 
So when hes By Sete Bu have once been obtained for 
O71 02 O11 


each test, they may be used for every pupil within the group. The 
process then becomes merely one of finding for each pupil the sum 
of the test scores after each is multiplied by a single constant, the 
quotient of the B divided by the sigma. The same sigmas were 
used for Group 3 as for Group 2 for the following reasons: 

1. The groups were of the same school grade, had been selected 
on the same relative intelligence basis, and were of approximately 
the same age. 

2. Assuming that the sigmas of the different tests were slightly 
different in Group 3, the change in variability for all the tests 
would be a fairly constant ratio. Hence, the correlation of the 
various factors with the criterion will not be materially affected. 

The combined weighted criterion scores for each pupil were next 
transmuted, for purposes of correlation on the chart devised by 
Dr. Herbert Toops. All the correlations in this study were done 
by the Toops’ method. 


The formula follows: 


S[(@X+2Y9 —2(X—Y)"]— (2X) x ZY) 


VN(2X)?—(ZX)2 VN(SY)?—(ZY)? 


The chart of Dr. Toops for plotting the scatter diagram consists 
of eighteen steps running from 0-17, inclusive. The method of 
transmutation is as follows: 

The lowest score made by any pupil in a group is subtracted 
from the highest score plus one. This gives the inclusive range. 
The inclusive range is then divided by 18 (the number of steps in 


Statistical Treatment jive 


the chart) and the quotient represented by the next higher integer 
taken as the class interval. The transmutation scale is then built 
up. Step 1 extends from the lowest score to a number which is 
equal to the lowest score plus one less than the class interval. 
Steps 2, 3, etc., are built up in the same manner. 

Tabulation and Transmutation of Factors. The same method 
of transmutation was used for the various items of the sixteen 
factors as for the criterion. The original scores of practically all 
items were expressed in definite numerical units so that they could 
be treated statistically without alteration. The following excep- 
tions need explanation. 

The elementary school marks were recorded in terms of the first 
letters of the alphabet. A transliteration was made on the follow- 
ing basis: 

A=6)b-—6>, b=45C=1. 
More involved formulae for the process are available,! but for 
practical purposes the above method is probably as reliable as any 
other. It is used by the Institute of Educational Research of 
Teachers College in its vocational guidance inquiry. A convenient 
scale for transmuting all the elementary marks, including the 
averages of two or more, extending from 10 to 60, was used. 

In the case of the various rankings: 

1. Ranking of pupils by teacher on 12 traits. 
2. Ranking by pupil of (a) importance of subject; (6) preference for 

subject; (c) preference for teacher, 
it will be recalled that 1 represented the highest score, 2 the 
next highest, and so on. In the statistical treatment, these values 
were reversed in order that the correlations might be expressed 
positively rather than negatively. 

Thus, 1=7, 2=6, 3=5, 4=4, 5=3, 6=2, 7=1. 

~ In the case of “ plan after graduation,” as shown previously, the 
pupil checked on the questionnaire one of six possible items: 


Score Assigned 


PEG AL EeNC CONOUR. Ss a ttn ete oe Pa ens, Sol dee ahik oes On on 6 
To attend teacher training or normal school. ............. 5 
PERE MEO PACE SCHOOL OREN eN CS PAS wee diac oietd ae eon aaa ole 
GPO SOL0e SDECIAD SCDOOL: 2. Seak\iecsick eckeswa «sale Delay at 4 
SO WORK Bie isemere ate erie as sig wy sb cle y lati c= foke se ieee rs 
‘oO go tower Way ir0Mm homies. hs chs. ves a caiue vase e 1 


1 Kelley, Educational Guidance. 


18 Detailed Factors in Latin Prognosis 


These items were ranked by a group of students of education on the 
basis of “academic interest”? and assigned the numerical values 
following each item. 

In the case of “‘plan for life” the four items: 


Score Assigned 


Business. ois ps as Re Saale s Cate ae ee Loe ee eee 3 
Trade x o:tic vas sho Beas he We ie ee is Cece bie eee ee eee Q 
Professions e320), eo ci aise ee eee 4 
Home foe et oe ey ee Oe ee eae 1 


were ranked in the same manner as above on the basis of “aca- 
demic interest,’ and assigned the numerical values following 
each. 

Inasmuch as the items of the sixteen factors were practically 
the same for the three groups, in building up the transmutation 
scales for both the criterion and the factors, a sufficiently large 
allowance was made in the inclusive range of the first group 
treated to include any probable scores in the other groups. A 
single exception to this is the I.Q. of Group 1, shown at the end 
of Table II. For Group 1, the transmuted scores of Dr. Allen 
were used for the criterion and the prognosis tests. 

Table II shows the gross scores corresponding to steps of the 
Toops’ chart in the combined weighted Latin criterion, and in all 
items of the various factors. The class interval is also given. 


2. Raw CoeEFFICIENTS OF CORRELATION 


Table III which follows shows the raw correlation of all vari- 
ables with the Latin criterion. The probable error is shown in 
each case. 

Obviously, no correction for attenuation was made, for in the 
case of many factors only one measurement was or could be possi- 
ble. Then, too, as Truman Lee Kelley! has indicated, correction 
for attenuation presumes an ideal relationship while the funda- 
mental aim in any prognosis study is to obtain data as they exist 
and can be secured under normal conditions. Dr. Allen, in the 
case of some of the psychological tests, corrected for attenuation 
but made no use of the corrections in his study, realizing their 
relative unimportance from the point of view of the practical 
administrator. 


1 Kelley, Educational Guidance. 


Step 


Class 


Interval 


Combined 
Weighted 
Latin 
Criterion 


858-890 
825-857 
792-824 
759-791 
726-758 
693-725 
660-692 
627-659 
594-626 
561-593 
528-560 
495-527 
462-494 
429-461 
396-428 
363-395 
350-362 
297-329 


33 


Factor I 
Briggs | Thorndike 
Alpha | Prognosis 

and Tests 
Beta A and B 
68-71 102-107 
64-67 96-101 
60-63 90-95 
56-59 84-89 
5200 78-83 
48-51 72-17 
44-47 66-71 
40-43 60-65 
36-39 54-59 
32-35 48-53 
28-31 42-47 
24-97 36-41 
20-23 80-35 
16-19 24-29 
12-15 18-23 
8-11 12-17 
4-7 6-11 
0-3 0-5 
4 6 


ScALE FOR TRANSMUTING THE CRITERION AND ALL Facrors TO THE Toors CHART 


Facror II| Facror III | Facror IV 

Inter- Hich School 

polation 1.Q. Age Gh di ay 

(ana? endance 
119-125 144-147 190-192 88-89 
112-118 140-143 187-189 86-87 
105-111 136-139 184-186 84-85 
98-104 1382-135 181-183 82-83 
91-97 128-131 178-180 80-81 
84-90 124-127 175-177 78-79 
77-838 120-123 172-174 76-77 
70-76 116-119 169-171 74-75 
63-69 112-115 166-168 72-73 
56-62 108-111 163-165 70-71 
49-55 104-107 160-162 68-69 
42-48 100-103 157-159 66-67 
35-41 96-99 154-156 64-65 
98-34 92-95 151-153 62-63 
Q1-27 88-91 148-150 60-61 
14-20 84-87 145-147 58-59 
7-13 80-83 © 142-144 56-57 
0-6 76-79 139-141 54-55 

of 4 3 Q 


TABLE II 


Facror V Factor VI | Facror VII Factor VII Factor IX Factor X Facror XI Factor XII 
Teachers’ Rankings 
. : : Plan : Time Combined 
Elementary Elementary ED Single Sum of | Minutes | Movie Daily After Flan Music Outside Worl Spent Study of 
Attendance ve et Rees Trait pean eres stipe Sleep | Grad- ro Lessons | Language Pp for on All Subjects, 
ea aEKs Fale aur uation arents Study Except Latin 
189-190 ere 95-99 my. 85-89 17 17 17 17 17 eg 34-35 102-107 
187-188 58-60 90-94 Goes es g0-S4 | 16 16 16 16 16 16 32-33 96-101 
185-186 55-57 85-89 15 55-57 | 75-79 | 15 15 15 15 15 15 30-81 90-95 aia 
183-184 52-54 80-84 14 52-54 | 70-74 | 14 14 14 14 14 14 28-29 84-89 280-299 
181-182 49-51 75-79 13 49-51 | 65-69 | 13 13 13 13 13 13 26-27 78-83 260-279 
179-180 46-48 "10-74 12 46-48 | 60-64] 12 12 12 12 12 12 24-95 79-77 240-259 
177-178 43-45 65-69 11 43-45 | 55-59] 11 11 11 rl 11 11 22-23 66-71 220-239 
175-176 40-42 60-64 10 40-42 | 50-54] 10 10 10 10 10 10 20-21 60-65 200-219 
173-174 37-39 55-59 9 37-39 45-49 9 9 9 9 9 9 18-19 54-59 180-199 
171-172 34-36 50-54 § 34-36 40-44 8. 8 8 8 8 8 16-17 48-53 160-179 ° 
169-170 31-33 45-49 7 31-33 | 35-39 ‘i i" 7 7 7 7 14-15 42-47 140-159 
167-168 28-30 40-44 6 28-30 30-34 6 6 6 6 6 6 12-13 36-41 120-139 
165-166 25-27 35-8 5 25-27 | 25-29 5 5 5 5 5 5 10-11 30-35 100-119 
163-164 29-94, 30-34 4 22-24, 20-24, A 4 4 4 A 4 8-9 Q4A—29 80-99 
161-162 19-21 25-29 3 19-21 | 15-19 3 8 3 3 3 8 6-7 18-23 60-79 
159-160 16-18 20-24 Q 16-18 | 10-14 2 Q 2 2 2 2 4-5 12-17 40-59 
157-158 13-15 15-19 1 13-15 5-9 1 i 1 1 1 1 2-3 Gu 20-389 
155-156 10-12 10-14 0 10-12 0-4 0 0 0 0 0 0 0-1 0-5 0-19 
Q 8 D 1 3 5 i 1 1 il 1 1 Q 6 20 


Preference 
Importance of Pupil 
of Subject for 
Subject 

Liv aye 
16 16 
15 15 
14 14 
13 13 
12 12 
11 11 
10 10 
9 9 
8 8 
7 7 
6 6 
5 5 
4 4, 
3 3 
2 Q 
1 1 
0 0 
1 1 


Preference 
of Pupil 
for 
Teacher 


17 
16 
15 


Cr wmwoePonwkms 


Factor XIII| Facror XIV | Facror XV | Factor XVI 


Extra- 
Curricular 
Activities 


SO WWE aArAaNtNe 


I. Q. for 
Group I 


189-195 
182-188 
175-181 
168-174 
161-167 
154-160 
147-153 
140-146 
133-139 
126-132 
119-125 
112-118 
105-111 
98-104 
91-97 
84-90 
77-83 
70-76 


Statistical Treatment 


SHowine Raw Cogrricients or CoRRELATION oF ALL VARIABLES 


TABLE III 


Wits Latin Criterion 


Factor I 
Prognosis Tests 
1. Briggs Analogies Alpha....... 
2. Briggs Analogies Beta........ 
3. Thorndike Word Knowledge A 
4. Thorndike Word Knowledge B 
HLNSETPOlAbiONu lint. oe. 2c 
Oremmterpolation’2...4,0-6 00. sore 


Facror II 
7. Intelligence Quotient........ 


Facror III 
8. Age 


Factor IV 
9. High School Attendance...... 


Factor V 
10. Elementary School Attendance. 


Factor VI 

Elementary School Marks in All 
ubjects 

1. Combined Average of Elemen- 

tary Reading, Grammar, Com- 

position, and Spelling........ 

12. Arithmetic (Average of Two 

INE a ee hoa (ERS ee 

13. Combined Average of History 

and Civics and Geography.... 

14. Combined Average of Penman- 

ship, Music, and Drawing.... 

15. Combined Cooking and Sewing 

PAWOTS GCS Ath tis kts nies 

A. Science alone for Group 3 

B. Shop alone for Group 3. . 

TG. Physical Training... 02). oo. % 

17. General Estimate............ 

18. Combined Average of 15 Marks 

PADOVG aisahe shel bin Cietlarctivs skate 


Facror VII 

High School Marks in All Subjects 
19. Semester Mark, Latin........ 
20. Semester Mark, English...... 
21. Semester Mark, Biology...... 
22. Semester Mark, Mathematics. 
23. Semester Mark, Civies....... 
24. Semester Mark, Drawing..... 
25. Semester Mark, Music....... 
26. Semester Mark, Physical Train- 

MIN s PEs aot et, hrs 8k cleelelee 


Boys’ HicH 


Corre- 
lation 


27. Semester Mark, Elocution.... 


Factor VIII 
Teachers’ Ranking of Pupils on 
Twelve Traits 

28. Teacher’s Ranking Persever- 
PIO OG ened wits Mosh tris pharm 

29. Teacher’s Ranking Industry... 
30. Teacher’s Ranking Earnestness 
31. Teacher’s Ranking Nerve Sta- 
ULL Veet a cn cate, ee eee 

32. Teacher’s Ranking Orderliness. 
33. perber Ranking Self-Confi- 
TIO Ge Cie a cw ole nis ate Sekt ete oie 


P. 
able Corre- 
Error lation 


-————— | —————————————_.- J. | | ——— 


ee ee 


0366 .4348 
0330 . 5034 
0404 .3001 
0408 1772 
0429 . 0847 
0450 . 3440 
0401 .4778 
0426 | —.3847 
0460 2684 
.0832 
3307 
3227 
2840 
2188 
. 3076 
.0955 
4368 
4088 
0281 8371 
0347 5182 
6964 
.0343 
.4030 
0443 1375 
0422 1054 
0458 1967 
5138 
5589 
5228 
3165 
5688 
. 5614 


W ADLEIGH 


Prob- 
able 
Error 


Corre- 
lation 


19 


Des Wirt CLINTON 


20 Detailed Factors in Latin Prognosis 


TABLE IlI—(Continued) 


Boys’ Hiau W ADLEIGH De Wirt CLINTON 
Corre- ers Corre- eaOrs Corre- eae 


lation | Frror | lation | Brror | lation | Error 


34. Teacher’s Ranking Accuracy. . .6334 | .0451 .6728 | .0364 
35. Teacher’s Ranking Right Atti- 

tude Toward Criticism....... 5472 | .0528 .5411 | .0470 
36. Teacher’s Ranking Frequency 

OF Hel pits tic cues nee eee cere .382388 | .0675 .3191 | .0597 
37. Teacher’s Ranking Promptness .5968 | .0485 .4850 | .0509 
38. Teacher’s Ranking Ability to 

Do Independent Work....... .6187 | .0465 .6788 | .0359 
39. Teacher’s Ranking Social and 

Moral vA Chitudes sol acs cic ete .4710 | .0587 .5426 | .0469 

Factor IX 


Study and Conditions for Study 
40. Minutes of Outside Help Daily 


On: Watiits neuekoce «oe .0132 | .0460 | —.0355 | .0753 | —.0970 | .0659 
41. Average Number of Movies per 
IW eels aaddion ae tae iets aeneete —.0872 | .0457 | —.1721 | .07382 | —.1664 | .0647 
42. Average Number of Hours of 
Sleep daily SeeraG sata cles soe —.0070 | .0460 | —.0585 | .0751 .1249 | .0655 
Factor X 


Individual Interests and Ambitions 
43. Academic Interest as Shown by 


Plan After Graduation....... —.0367 | .0459 .1989 | .0739 .1850 | .0642 
44, Academic Interest as Shown by 
Piansformlile rns eee cece —.1727 | .0446 | —.1252 | .0742 .0275 | .0664 
Factor XI 


Outside Work 
45. Time Spent Weekly Taking 

Music bessons? i.e sa cence .0323 | .0460 .1770 | .0730 .0880 | .0660 
46. Time Spent Weekly on Any 

Outside Language or School 


SuDjeCtam che oie een ee .0979 | .0456 .1190 | .0743 .1042 | .0658 
47. Time Spent Weekly in Work 
FOr UPAreNLS wee eeateee nese eter —.0439 | .0459 | —.0058 | .0754 | —.1029 | .0658 
Facror XII 


Amount of Home Study 
48. Average Time Spent in Study 


Daily baglish soda ee er .0778 | .0457 | —.2496 | .0707 | —.1456 | .0651 
49. Average Time Spent in Study 

Daily sloatina em arenes —.1540 | .0449 | —.1433 | .07389 | —.1859 | .0642 
50. Average Time Spent in Study 

Dailyeiology:cte eee oe —.2424 | .0710 | —.0702 | .0662 
51. Average Time Spent in Study 

Daily, Mathematics......... .1616 | .0448 .0469 | .0664 
52. Average Time Spent in Study 

Dailys-Civicse sean cere —.0598 | .0458 | —.2552 | .0705 .1056 | .0658 
53. Average Time Spent, English 

Plus Civics, Plus Biology. . —.2975 | .0687 | —.0515 | .0663 


54. Average Time Spent, English 
Plus Civics, Plus Biology, Plus 
Mathematics. os. <ce se iee< .1095 | .0454 


Facror XII | : 
55. Pupils’ Ranking of Latin on 
Basis of Importance......... —.1014 | .0455 .1603 | .0735 .1397 | .0652 


Facror XIV 
56. Pupils’ Ranking of Latin on 
Basis of Preference.......... .2705 | .0426 1416 | 0739 .5154 | .0488 


Factor XV 
57. Pupils’ Ranking of Teacher on 
Basis of Preference.......... .0984 | .0456 | —.0361 | .0753 .3833 | .0567 


Factor XVI 
58. Pupils’ Participation in Extra- 
curricular Activities......... .0144 | .0460 .0812 | .0749 | —.0374 | .0664 


Statistical Treatment 21 


38. SIGNIFICANCE OF RAw CorRRELATIONS 


Factor I. Scores Made in Each Test. 


Of all the objective factors used in this experiment, Briggs 
Analogies tests, either Alpha or Beta, offer the best single basis of 
prognosis. It will be observed that the correlations for these 
tests in all three groups approximate .50. Of all the prognosis 
tests, Briggs Analogies show the greatest consistency in the three 
groups. ‘Thorndike Tests of Word Knowledge have a much lower 
correlation and vary a great deal more. The correlations of the 
Rogers Interpolation Tests run fairly high with the De Witt Clin- 
ton group but are very erratic when the three groups are con- 
sidered. 

It will be recalled that Dr. Allen used 364 pupils, and that this 
study deals with 215 who were still in school the following year. 
It is interesting to observe the change made in the correlations by 
the loss of the 149 pupils from the original group. Table IV 
below shows Allen’s correlations with 364 pupils, and the writer’s 
correlations with the same data after 149 were dropped from the 
list. 

TABLE IV 


SHowine (a) ALLEN’s ORIGINAL PRoGNosis CoRRELATIONS WITH 364 PUPILS AND 
(b) CoRRELATIONS OF SAME DATA FoR 215 OF THE SAME PUPILS 


Allen’s Correlations | Writer’s Correlations 


1. Briggs Analogies Alpha.......... Bist] 4502 
2. Briggs Analogies Beta........... .56 .5314 
3. Thorndike Word Knowledge A... se 3488 
4. Thorndike Word Knowledge B... :a8 soot 
5. Rogers Interpolation1.......... 29 . 2613 
6. Rogers Interpolation 2.......... . 23 . 1452 


Y The above figures show the tremendous effect of selection upon 
a correlation coefficient, and consequently indicate the major dif- 
ficulty in an experimental investigation of this character. To 
obtain high coefficients of correlation it is necessary to measure 
heterogeneous groups. Some individuals should be of high, some 
of low, and some of mediocre ability. In the secondary schools, 
however, the pupils at the beginning of the first year are already 
highly selected. In the second place, Latin itself selects on some 
basis. Finally, and of great importance, is the fact that criterion 


99 Detailed Factors in Latin Prognosis 


scores are obtained only from those who remain in school until 
the end of the semester. Hence, all the correlations in Table III 
above are much lower than they would be if we could get an exact 
measure of all pupils, those who drop out as well as those who 
remain until the end of the semester. 


Factor II. Intelligence Quotient. 


In most investigations thus far the I.Q. has a correlation with 
achievement in academic subjects of from .40 to .60. The lower 
correlations in Dr. Allen’s group of 215 pupils still in school the 
second year would seem to indicate that the high school selects 
on the basis of intelligence. This is the common impression. 
OBrien’s investigation and Book’s! recent study in Indiana led 
them to disprove this common impression, yet the unpublished 
results of Dr. Colvin’s recent study in Massachusetts disagree 
with Book, and substantiate the position that the high school 
selects on the basis of natural ability. 


Factor III. Age. 


Age seldom if ever, in grade groups, gives other than a negative 
correlation with academic success. Thus, the correlations with 

Latin in this study are typically what we should expect. The 
- brighter pupils get into high school earlier because they are bright. 
The De Witt correlation of —.57 is unusually high. Kelley? found 
a correlation of —.31 between average class standing and age. 
Fretwell*® found a correlation of —.34 between age and school 
marks the first year of the junior high school. 


Factors IV anp V. High School and Elementary School Attend- 
ance. 


High school attendance and elementary school attendance ap- 
pear relatively unimportant factors in success in first year Latin. 
Although this is empirically true, few doubt the effect of long 
periods of absence. Long periods of absence usually mean elimina- 
tion, and hence no criterion measures at all are secured. In fact, 
then, our empirical investigation deals for the most part only with 
those who have little absence. It seems fairly evident from this 
experiment in first year Latin, and other experiments, that if we 


1 Book, William F.: The Intelligence of High School Seniors. New York, 1922. 
2 Kelley, Educational Guidance, p. 73. 
3 Fretwell, A Study in Educational Prognosis, p. 15. 


Statistical Treatment 23 


use criterion measures for those pupils only who finish the semester, 
both elementary and high school attendance have little of prognos- 
tic value. 


Factor VI. Elementary School Marks. 


Elementary school marks have very important value as instru- 
ments of prognosis in first year Latin. Kelley and others have 
found similar results in the case of other academic subjects. Of 
the groupings of elementary subjects shown in Table III, it can be 
seen that the “combined average of all marks”’ and the “‘general 
estimate’? mark are the best predictors. Of the single subjects, 
arithmetic and English should be given precedence. Physical 
training, penmanship, music, and drawing have the lowest corre- 
lations. Common experience would probably agree that Latin 
and these subjects have comparatively few common elements. 
The low correlations may also be explained in part by the fact that 
teachers of these subjects do not distribute the marks widely. The 
marks cluster around the central tendency. 

From the point of view of securing very high correlations, the 
last mentioned difficulty plays havoc with all the elementary marks. 
It is a fairly rigid requirement that for a pupil to be promoted in 
the New York City schools, he must have a minimum mark of B. 
Hence, for the most part, only three marks, B, B plus, and A, 
are used. This practice prevents high correlations in two ways: 
(1) As explained above, it selects only the best pupils. (2) It 
places the best, when selected, within a narrow scale. 


Factor VII. High School Marks. 


High school marks for the semester, other than Latin, rank by 
subject in practically the same order as corresponding subjects 
of the elementary school. The correlations of high school marks, 
due to recency in time, are much higher.!. Mathematics and Eng- 
lish rank at the top; and drawing, music, penmanship, physical 
training at the bottom. Biology, .55-.70, with a correlation 
even higher than mathematics, would suggest that in character of 
content or in nature of study required, it appears to have many 
elements in common with Latin. The De Witt Clinton group was 
the only one studying elocution. The correlation, .63, is surpris- 
ingly high. 


1 Kelley: Educational Guidance, p. 11. 


24 Detailed Factors in Latin Prognosis 
Factor VIII. Teachers’ Rankings of Pupils. 


The correlations of teachers’ rankings of pupils on the twelve 
traits are all consistently high. Frequency of help, with .32, is the 
lowest. The closeness of correlation of the various traits would 
seem to indicate that the teachers did not distinguish closely be- 
tween them, that if a pupil were given, for example, “5” on indus- 
try, the tendency was to give him “5” on all others. However, 
we should expect a reasonably high correlation between teachers’ 
judgments of desirable traits. 


Factor IX. Study and Conditions for Study. 


The amount of help which a pupil receives outside of school on 
Latin seems in itself to be a negligible factor. Not only is the 
correlation negligible, but the pupils actually receive little help 
outside on Latin. Only 6 in Group 1, 15 in Group 2, and 14 in 
Group 3, report any help at all. For the Wadleigh and De Witt 
Clinton groups the correlations are slightly negative. These 
correlations are not startling for the reason that the duller a pupil, 
the more help he will probably need. 

The correlations for the average number of movies attended per 
week are negative in the three groups, interestingly close in Groups 
2and 3. They would seem to justify in part the common assump- 
tion that the more movies pupils attend, the poorer they do in their 
work. Which is the cause and which the effect is a subject for 
controversy. The correlations are not large enough to be par- 
ticularly significant. | 

The average number of hours of daily sleep, as reported by 
pupils, appears of little consequence. The correlations for the 
three groups fluctuate around 0. 


Factor X. Individual Interests and Ambitions. 


Academic interest, as shown by plan after graduation, gives 
positive correlations worthy of consideration for Groups 2 and 3. 
The correlation of Group 1 has perhaps been vitiated by the lapse 
of a year of time between the criterion score and the securing of 
the information. The lowness of the correlations is evident when 
the distributions are observed. Only 10 pupils in Group 1, 16 in 
Group 2, and 9 in Group 8, did not intend to go to college. Latin 
in these schools selects those who intend to go to college. The 
smaller proportionate number in Group 1 (to whom the question- 


Statistical Treatment 25 


naire was given the second year) who do not intend to go to col- 
lege, would suggest that in so far as Latin pupils are concerned, 
the second year of the high school selects on this basis. 

The correlations for academic interest, as shown by plan for life, 
are not significant because of the same lack of distribution just 
mentioned. Only 22 in group 1, 14 in Group 2, and 8 in Group 8, 
did not mark “profession” as the choice for life work. 


Factor XI. Outside Work. 


The correlations for music are slightly, but not significantly, 
positive. This may mean that the musical pupils are the brighter, 
or that they are the more ambitious. Of the 398 pupils in this 
group, 138 took music lessons. 

The suggestion above, relative to music lessons, applies equally 
well to the study of any language or school subject outside of 
school. Forty-one in Group 1, 7 yn Group 2, and 15 in Group 3 
pursued the study of some language or some school subject. The 
study of Hebrew was the most important subject pursued. 

The correlations for time spent weekly in work for parents in 
all the groups are negative, but virtually negligible. However, 
the slight consistent negativeness may have important sociological 
implications. 

No correlations were computed for the time spent on outside 
work for those other than parents, because too few did any out- 
side work. 


Factor XII. Amount of Home Study. 


Most of the correlations for the time spent in study are nega- 
tive. This is naturally what we should expect in subjects other 
than Latin: that, as pupils spend more time in other subjects, they 
do poorer in Latin. But the correlations for Latin itself are con- 
siderably and consistently negative. Hence, we may reasonably 
infer that the pupils who did poor work in Latin studied more be- 
cause they were dull. 


Factor XIII. Pupils’ Ranking of Importance of Subject. 


The correlations for the ranking of Latin on the basis of impor- 
tance, for Schools 2 and 8, are positive, but not large. The neg- 
ative correlation in the case of Group 1 is difficult to explain. The 
lapse of time, mentioned previously in the case of other items with 
this group, may be an important factor. 


26 Detailed Factors in Latin Prognosis 


Factor XIV. Pupils’ Ranking of Preference for Subject. 


The correlations for preference of subject are fairly significant. 
The pupils of Group 3 were all taught by one teacher, and the 
high correlation of “‘preference for subject”’ and “preference for 
teacher”? would indicate that both the subject and the teacher 
were popular with the pupils. 


Factor XV. Pupils’ Ranking of Preference for Teacher. 


The correlation of ranking of teacher on basis of preference has 
just been commented upon in the case of Group 3. The correla- 
tions of Groups 1 and 2 would indicate that preference for teacher 
has negligible effect upon a pupil’s success in first year Latin. 


Factor XVI. Participation in Extra-Curricular Activities. 


The correlations of participation in extra-curricular activities 
for the three groups fluctuate closely around zero. The zero corre- 
lations in this case are no doubt caused by the presence in this 
factor of many counter-balancing forces. For example, those 
pupils who are bright, who make high scores on the Latin crite- 
rion, and who are versatile in extra-curricular participation, will 
tend to raise the correlation. On the other hand, pupils who may 
be prevented from making good scores on the Latin criterion be- 
cause of their diversity of extra-curricular interests, will tend to 
lower the correlation. 


4. Errect of DETAILED Factors AS SHOWN BY MULTIPLE RatTIo 
CORRELATION COEFFICIENTS, AND SELECTION OF 
Proenosis Factors 


\ As set forth in the statement of the problem in Chapter II, the 
‘specific purpose of this study is, “To find the influence of certain 
detailed factors upon a pupil’s success in first year Latin, to choose 
the most effective factors, and through multiple correlation to 
obtain their combined effect as a basis for prognosis.’ “‘A multiple 
correlation coefficient is that correlation which expresses the total 
efficiency of the scale when tests chosen are those that bear the 
best or highest correlation with the criterion.”’! 

The contribution to a multiple correlation coefficient which any 
factor makes depends upon two considerations: 


1 Burr, Emily Thorp: Psychological Tests Applied to Factory Workers, p. 73. 
Doctor’s dissertation, Columbia University, May 1922. 


Statistical Treatment Qy 


1. The correlation of the particular factor with the criterion. 
2. The intercorrelation of the particular factor with other vari- 
ables used. 


Hence, to the investigator in prognosis, the desiderata of a good 
test or an effective factor are, first, that it should correlate highly 
with the criterion; second, that it should have a low correlation 
with other factors. The first is obvious. The second is evident 
when the meaning of a multiple coefficient is recognized. To 
build up a multiple coefficient for prognosis, it is necessary to 
measure many elements of the ability we desire to predict./ Differ- 
ent tests or factors measure different elements to the degree that 
their intercorrelations are low. Empirically, two factors having 
an intercorrelation of plus 1.00 would measure the same elements, 
and have no more value than either singly. 

The formula used for the multiple ratio correlation coefficients 
in this experiment is that of Dr. Toops: 


tio! = i einen ican. ruc) 
1—- ruc 
The formula gives correlation coefficients slightly less than the 
true multiple but a very close approximation to it. It is an al- 
gebraic transmutation of some of the older formulae, designed to 
economize time. By the method it is possible to find the specific 
effect of each of a number of factors in combination, to select the 
most effective or desirable factors and build up a multiple ratio 
correlation coefficient, without computing all the intercorre!ations 
at the beginning of the process. ‘The total number of intercorrela- 


tions for any series of variables—n—is equal to pool To 
compute all the intercorrelations with three groups of pupils and 
the number of variables used in this study would be an almost 
prohibitive task. By the multiple correlation ratio, the process 
is greatly reduced. An explanation of the terms used in the 
equation follows: 

I =criterion. 

C =combination of one test (existing at beginning of process). 

C’ =desired combination (formed by adding a factor to C). 

U =“‘unique” (text or factor added). 

ric’ =correlation of criterion with desired combination. 

ric =correlation of criterion with combination. 


28 Detailed Factors in Latin Prognosis 


rip =correlation of criterion with “unique.” 
ryc=correlation of “unique”? with combination. 


As stated above, the contribution of a factor to a multiple 
correlation coefficient depends upon its correlation with the cri- 
terion and with other factors. The formula above, when analyzed, 
contains only these two elements. Hence, algebraically, the 
effectiveness of a factor depends upon its comparative ability to 
function in the above formula, that is, to raise the coefficient of 
correlation. 

Two questions arise in regard to the use of the formula. First, 
what is C (combination existing at the beginning of the process) 
and how is it secured? Cy, in the beginning, is the basic test to 
which others (“uniques’’) are added. The factor is selected as 
the basic one which has the highest correlation with the criterion. 
The second question is concerned with weighting. ‘The basic test 
is given a weighting of 1.00. The weighting of the second test 
and the amount which it adds to the basic factor is found by putting 
the proper correlations through the ile formula: 


C 
Us roe Me etue 
CO 10 Ti ue 
The third test is added at weight given by the following formula: 
gil nee aaa 
tTio-tiu * Tuc 

By the use of the above formulae four things have been done in 
this experiment: 

A. The Allen prognosis battery of six tests: Briggs Alpha, 
Briggs Beta, Thorndike A, Thorndike B, Interpolation 1, Inter- 
polation 2, have been combined for the Wadleigh and De Witt 
Clinton groups. 

B. The Wadleigh Group has been used as a trial group for locat- 
ing and evaluating basic factors most probably significant in the 
three groups. 

C. The four basic factors chosen in the Wadleigh group: Briggs 
Beta, Age, Thorndike B, and Elementary Average, are combined 
and the efficiency of the combination in predicting the criterion 
tested for each group. 

D. To these four basic factors in each group other factors are 
added, and tested for their contribution. 


61 = VW, +2 zrey Wa TAA 


Statistical Treatment 29 
A 


ALLEN Battery MUurtTIPLE COEFFICIENTS 


Dr. Allen, by combining the six prognosis tests, secured with 
364 pupils a multiple ratio correlation of .588. By combining the 
same tests for the Wadleigh and De Witt Clinton groups, coeffi- 
cients of .5633 and .6673 respectively are secured. Tables IV 


and V give for the Wadleigh and De Witt groups the following 
data: 


1. Correlation of each prognosis test with the criterion. 

2. Intercorrelations of the prognosis tests. 

3. Cumulative multiple ratio correlations of the accumulating 
combination (first test; first plus one added, etc). 

4. Amount each test adds to the previous multiple ratio corre- 
lation coefficient. 


Table IV should be read as follows: The correlation of Alpha 
with the criterion is .4348; its intercorrelations with the prognosis 
tests are: Beta .8990, Thorndike B .5829, Thorndike A .5534, 
Interpolation 1 .1822, Interpolation 2 .3878. The multiple ratio 
correlation coefficient produced by adding Alpha to Beta is .5055. 
The amount which Alpha contributes to Beta in combination is 
.0021. 

TABLE IV 


SHow1nG Aut TEstTs OF THE ALLEN Procnosis BATTERY IN COMBINATION 
WaADLEIGH GROUP 


INTERRELATIONS 

a ee COLTON Al ant 
Cri- ra oe Added 

Test terion § _| Inter- | Inter- ombl1- to 

(3c) | Briggs | Briggs Nae etd pola- | pola- | Ration Trot 

dike dike : : (re) IC 

Beta | Alpha B A tion tion IC 
Briggs Beta...| .5034 .8990 .6014 .6160 2155 38942 . 5034 

Briggs Alpha..| .4348 | .8990 POST OUGa | aE Looe tose: Is O00D .0021 
Thorndike B..|} .1772 | .6014 } .5829 .9128 | .0950 | .2451 | .5270 .0215 
Thorndike A..| .3001 | .6160 | .5534 | .9128 .0982 | .2564 | .5367 .0097 
Tnterme tae: SOS4 7 elo wlece «|e O900) 20982 iPass a) qipwi7 .0010 
Interp. 2......] .38440 | .38942 | .38878 | .2451 | .2564 | .6263 . 5634 .0257 


It will be observed from Tables IV and V that the correlation 
.588 of Allen’s prognosis battery with the criterion is approxi- 
mately midway between the Wadleigh correlation .5634 and the 
De Witt Clinton correlation .6672. This would seem to indicate 


30 Detailed Factors in Latin Prognosis 


that with different groups of pupils the Allen prognosis battery of 
tests assures a valid prediction of approximately .60 with the 
criterion. 

TABLE V 


SHow1nG ALL TESTS OF THE ALLEN PrRoGNosis BATTERY IN COMBINATION 
De Witt Cuinton Group 


INTERCORRELATIONS 
A a Corre- Amount 
Cri- lation | Added 
Test Vane ; Thorn- | Thorn-| Inter- | Inter- Shree to 
Ic Briggs | Briggs dike dike pola- pola- Tro! 
Beta | Alpha B Pe von oe ("1") 
Briggs Beta...| .4721 8640 | .2873 | .2453 | .4041 | .4412 | .4721 
Briggs Alpha..| .5179 | .8640 "3153 | .2879 | .4391 | .4587 | .5202 | .0481 
Thorndike B..| .4765 | .2873 | .3153 "8205 | .1159 | .1973 | .6154 | .0952 
Thorndike A..| .5123 | .2453 | .2879 | .8205 2007 | .2670 | .6325 | .0171 
Interp,1..... ‘4143 | .4041 | .4391 | .1159 | .2007 8043 | .6669 | .0344 
Interp.2.....| .4231 | .4412 | 4587 | .1973 | .2670 | .8043 6672 | .0003 
B 
SELECTION OF “Basic Factor COMBINATION” FROM WADLEIGH 
GROUP 


The checking of Allen’s experiment and the validity of the 
prognosis tests is an important outcome of this study. But it is 
only one phase of the main problem. “The aim of the present 
study is to find the influence of many possible factors including 
the Allen battery of six tests.”’ From the beginning of this study, 
two types of factors were recognized: first, those of a purely pre- 
dictive value, i. e., factors for which data could be secured for 
any pupil before he began the study of Latin; second, those factors 
which affect a pupil’s Latin product. In general, the first type 
of factor tells what capacities a pupil should have in order to suc- 
ceed, and may be thought of as “effective”’ factors. The second 
type of factor shows the influence of specific conditions upon the 
achievement of a pupil of given capacity, during his study of 
Latin, and may be designated as “affective” factors. The pro- 
cedure in this experiment has been to give first consideration to 
those factors of a purely predictive character; second, to add 
“affective” or relational factors. 

The Wadleigh group was used as a trial group for locating and 
evaluating basic factors most probably significant in the three 
groups. Of the items considered in the experiment, the following 


Statestical Treatment 31 


17 belong to the predictive type. Of these 17, Briggs Beta showed 
the highest correlation with the criterion, .5034. Hence, it was 
taken as the basic factor. Each of the other 16 items was then 
combined and tested for contributions, with Briggs Beta. The 
results are shown in Table VI following. Table VI should be read 
as follows: The correlation of Alpha with the criterion is .4348, 
with Beta .8990. The correlation produced by adding Alpha to 
Beta is .5055. The amount which Alpha adds to Beta is .0021. 


TABLE VI 


SHOWING TeEestInG oF 16 PrepictrveE Facrors ror AppitTion To Briees Brera 
WADLEIGH GROUP 


Amount 

(Pa) | re(Beisy |) Gio) | See 
5034 
SAS Gi = Pus RS 2 agg eR a .4348 . 8990 .5055 .0021 
ESSAI ROSA ead ores aed > soe 3001 6160 5037 0003 
MT DOIK OUI on ta ig Aa oe a's Ae ese rayge: 6014 5318 0284 
PCE TMRLION! 1. dha thts Gis cess okate .0847 . 2155 . 5040 . 0006 
PAbetHOlalolr o..,, eset oh os ee . 3440 . 8942 <OS7TT 0243 
1 AE AD co ch Meet RE Coe Naa 4778 .6071 . 5481 0447 
Elementary Attendance......... . 0832 .0689 .5057 .0023 
Poor Retr’ Ge 5). eee ke: . 3307 4549 . 5061 .0027 
HABE RMEE NG oe nek OE Bhs lad ao da o227 S417 - 0235 0249 
Preeti Gl atid Gris. titre 2. es . 2840 3376 .5179 0145 
Beton Dr) ee eo oe, ve . 2188 . 1033 . 5306 0272 
He TSO Le Cet BSD Ne Bite tat ea ea . 3076 . 3053 . 5288 0254 
Reveal: Uraining).. &. sug. c ee nee .0955 . 2639 .5048 .0014 
Greneral Eatimate 226i. oc. ea .4368 4551 5549 .0515 
Elementary Average............ . 4088 4451 5440 0406 

FY eee > SR oe a — 3847 — .0798 .6107* .1073* 


From Table VI we observe that age makes by far the most 
effective contribution, raising Beta from .5034 to .6107. Briggs 
Alpha adds practically nothing when Beta is in the combination. 
The same relation exists between the two forms of the Thorndike 
tests, as shown throughout this experiment. The two forms of 
each pair have a high self-correlation. Allen, with one from each 
of the three pairs of the prognosis tests in combination, secured 
with the criterion a correlation of .578, practically as high as with 
all six tests. 

General estimate, which is a rating of the elementary teacher 
and principal, ranks second, with I.Q. and elementary average a 


32 Detailed Factors in Latin Prognosis 


close third. Elementary attendance is relatively unimportant as 
would be expected from the low criterion correlation. Arith- 
metic makes the greatest contribution among the academic sub- 
jects. The non-academic subjects in the combination seem more 
effective than the academic. The reason will be suggested later. 

Age was next placed in the combination, and the remaining 15 
items tested for inclusion as the third factor. Table VII shows 
the results. 

TABLE VII 


SHowinGe Trestinc or 15 PrepictiveE Facrors ror ADDITION TO COMBINATION 
(Briacs Beta anp AGE) 


WaADLEIGH GROUP 


Amount added to 
Ty (Age) (Tio) Briggs Beta and 


Age, .6107 
ATTA Cremer e Le ao rrie can aa Meee —.1108 . 6129 . 0022 
PLHOFOCIKG Au wutnne tas be weertie cutee — .0515 .6110 .0003 
Mhoriike: Byes be as ee — .0212 . 6249 .0142 
Titerpolation: } iac.c cee wate os ee — .0637 .6121 .0014 
Interpolation 2ieq. boa so toe — .2209 .6170 .0063 
TU Ses ELE Ny, iP OG ery eee — .5708 .6110 .0003 
Elementary Attendance............. — .0004 .6128 .0021 
ANC RSG? Ce Sy ip eee Bw — 2537 6115 0008 
Aribhiinetic £4, jhe s eee Pies.) Se — 2341 . 6168 .0061 
ACE Cs G oie. meee oe ee — .1490 .6155 .0048 
Axi (BAM DEY Osc ae ee oe — .0042 | .6336 0229 
Ata Heit aie hed Se hh ey a Bee .0827 .6410* .0303* 
Piysieal Al pairing 3. 2 aang ons ae — .0723 . 6134 .0027 
General Nstimate, } 2 ase 8. oe — .2796 .6275 .0168 
Elementary Average................ — .1622 . 6306 .0199 


Inasmuch as age enters into the I.Q., it appears that when age 
is in the combination, I.Q. ceases to function. On first, but not 
second thought, it would seem startling that the sewing and cook- 
ing average stands first in the above table. “If you wish to pre- 
dict a pupil’s success in first year Latin, secure her elementary 
sewing and cooking marks”’ would appear humorous to most Latin 
professors. Why does sewing and cooking come out ahead of, for 
example, arithmetic, or average (R, G, C,S)? It is evidently be- 
cause of its low intercorrelation with Briggs Beta. These last- 
named subjects, as shown by the criterion correlations, page 31, 
have more in common with Latin than sewing and cooking do, but 
they also have more in common with Briggs Beta. Hence, when 


Statistical Treatment 33 


Briggs Beta is already in the combination, sewing and cooking 
make the greater contribution. Elementary average stands sec- 
ond, with Thorndike B a negligible amount less. 

Thorndike B was next placed in the combination. It was given 
precedence over sewing and cooking because of the less objective 
nature of these marks; also, incidentally, because the other two 
groups did not have sewing and cooking. It is probably more 


objective than elementary school average, and requires less labor. 
Table VIII shows the results. 


TABLE VIII 


SHOWING TESTING OF 14 PREDICTIVE Factors ror ADDITION TO COMBINATION 
(Briaes Bera, AcE, THORNDIKE B) 


WaADLEIGH GROUP 


Amount added to 
7, (Thorndike B) Les) Briggs Beta, Age, 
Thorndike B, .6249 


Briggs Alpha............... 5829 6249 .0000 


PETIGEDTUIKG GN | ose tee tocoe hn « .9128 . 6322 .0073 
Prlerpolraligne) sus vee eee .0950 . 6263 .0014 
AMTERDOIRLION: 2. .2 5p ak os = 2451 .6318 . 0069 
SCIP C Re etna td etiae Lo eate 3 7219 . 6276 .0027 
Elementary Attendance...... . 0304 . 6270 .0021 
MORO GE S\uee 3606 6269 0020 
Mthichicees, <6 Fieeo cs .1527 . 6299 .0050 
Cite AGS) ee ae . 3361 .§332 . 0083 
Tee TO Aiea eee 0560 6479 0230 
Av. (S and Citak eee eee . 2509 .6618* .0369* 
Physical Uraming; 72228... 2571 . 6259 .0010 
General Estimate........... .4330 6477 0228 
Elementary Average........ . 3278 6484 0235 


With the exception of sewing and cooking, elementary average 
with a correlation of .6484 stands highest. The other items re- 
main in about the same relative position as in the preceding tables. 

From an examination of the multiple ratio correlations of the 
foregoing tables, it is evident that the four most objective and 
most consistently outstanding factors are: Briggs Beta, Age, 
Thorndike B, and Elementary Average. They should go into the 
combination in this order; yet the results would be probably not far 
different, no matter in which order they were combined. An 
examination of the criterion correlations of these four factors for 
the Boys High and De Witt groups indicates, by and large, a close 


34 Detailed Factors in Latin Prognosis 


correspondence. Allowing for certain evident reasons for dis- 
crepancy (such as the lowering of the Boys High correlations by 
the selection of those still in school at the end of the third semester) 
we should expect from the four factors comparable multiple ratio 
coefiicients. ‘The procedure follows in Section C. 

For purely experimental reasons, however, it was decided in the 
case of the Wadleigh group to add to Briggs Beta, Age, and Thorn- 
dike B (giving sewing and cooking precedence over Elementary 
Average) three more of the original 17 items, solely on the basis of 
the amount they would add to the highest multiple ratio correla- 
tion coefficients. The three items proved to be: Average (sewing 
and cooking), Physical training, Average (penmanship, music, and 
drawing). Tables IX, X, and XI show the results. 


TABLE IX 


SHowine Testine or 13 Prepictive Factors ror AppDITION TO COMBINATION 
Brices Brera, AGE, THORNDIKE B, AVERAGE (SEWING AND COOKING) 


WADLEIGH GROUP 


Amount added to 
Briggs Beta, Age, 


7, (Sewing and (r,)  |Thorndike B, Sew- 
Cooking) ing and Cooking, 
.6618 
Brigze Aina <, Soc wee ee . 2030 . 6626 . 0008 
PPRorndike®A. Sy. bitciae nes . 3020 . 6629 0011 
Piterpoisuonl . os, kee ee — .0148 . 6626 .0008 
Interpolation’ 622.4 .< tthoe . 1268 . 6663 . 0045 
DP ORS Foon tt eee nee 1754 . 6629 0011 
Elementary Attendance..... .3461 . 6622 . 0004 
AVALR GAR, 'S)o eile nt 4938 . 6646 . 0028 
ATIENMICHG? sb Se er eae ee . 1582 . 6642 . 0024 
Ary (Hy CRG ate Ge ka) au eat . 5394 . 6620 . 0002 
AVG PAVED pry eee Slee 4699 .6657 .0039 
Physical ‘Traming:: is. 2. ./..% 4523 .6754* .0136* 
General Estimate........... . 5232 . 6648 . 0030 
Elementary Average........ .6918 . 6622 . 0004 


When the remaining items are tested for their contributions to 
the combination: Briggs Beta, Age, Thorndike B, (Sewing and 
Cooking), Physical Training, (Penmanship, Music, and Drawing), 
none of them make contributions worthy of consideration. General 
Estimate, .6903, which stands highest, adds only .0029. It might 
be possible by placing a few more factors in the combination to 
raise .6903 to .70 or more, but the effort as shown by the above 


Statistical Treatment 


TABLE X 


35 


SHowine Testine or 12 Prepicrive Facrors ror ADDITION TO COMBINATION 
Briaes Bera, Ack, THornpike B, Sewine AND CookinG, PuysicaL TRAINING 


WaADLEIGH GROUP 


r,, (Physical feo, 
Training) Le 

RIA OS TASS ok eh oe «ates . 2095 . 6764 
PE ROTUCIKGPA yy os ee aes as . 2164 .6773 
BALLET POLALION Li ato ysis sien 4 . 1643 .6756 
Teter pormvtlon 22" ate ts Gl . 0322 . 6782 
| UE Re SR a aie ir . 1303 . 6756 
Elementary Attendance...... . 38019 .6755 
canis 8158 Cok GR) Ia ole Sane ae . 5099 6754 
APIRIINOUG LE st. fue ec ce «> . 2621 . 6796 
Ged 2 Oa C) eet ee 4485 6763 
on EA tS ES Oe ge ek Be 4758 .6874* 
General Estimate........... . 5564 .6857 
Elementary Average........ . 6749 . 6827 

TABLE XI 


Amount added to 

Briggs Beta, Age, 

Thorndike B, Sew- 

ing and Cooking, 

Physical Training, 
. 6754 


.0010 
.0019 
. 0002 
. 0028 
. 0002 
. 0001 
. 0000 
, 0042 
. 0009 
.0020* 
. 0003 
. 0073 


SHOWING TESTING oF 11 PreEpictive Facrors ror ADDITION TO COMBINATION 
Brices Brera, AGE, THORNDIKE B, (SEWING AND Cooxina), PHysicaL TRAIN- 


ING, (PENMANSHIP, Music, Drawine) 
WaDLEIGH GRouUP 


r_,(Penmanship, ee) 
Music, Drawing) i 


RIPIBOSPA LDN Sica. ees aes .0401 .6877 
PE HOINOIKE A. | cisco s ce Ze tine <> . 0680 . 6891 
interpolation | os foes 0473 .6877 
Interpolation’... a8 .0703 . 6899 
Pe eS oe ot ee a — .0019 . 6882 
Elementary Attendance...... . 2086 . 6875 
WA ast ties Cre Cae) Sa ae wink es . 3886 . 6896 
PPAR IIDENAG is ee nas sane 8 , 2512 . 6890 
TA 1 U8 bad GAGE Deane Oe ae , 8548 . 6875 
General Estimate........... .4566 .6903* 


Elementary Average........ . 6082 .6877 


Amount added to 
Briggs Beta, Age, 
Thorndike B, Sew- 
ing and Cooking 
Physical Training, 
(Penmanship, 
Music, Drawing) 
. 6874 


. 0003 
.0017 
. 0003 
. 0025 
. 0008 
.0001 
. 0022 
.0016 
. 0001 
.0029* 
. 0003 


36 Detailed Factors in Latin Prognosis 


experimental procedure would not be justified. The accretions are 
too small and, as previously stated, the data are not sufficiently 
objective for a prognosis scale. A correlation of .69 is the correla- 
tion with the Latin criterion, secured in the case of the Wadleigh 
group, when factors are selected regardless of objectivity, solely 
on the basis of how much they will add. 


C 
TrEstTInG oF Four Basic Factor CoMBINATION FoR Eacu Group 


The four basic factors selected in the Wadleigh group: Briggs 
Beta, Age, Thorndike B, and Elementary Average, were placed 
in the combination and tested for each of the other groups. Table 
XII shows the intercorrelations of the four factors for the three 
groups. 

TABLE XII 
SHOWING INTERCORRELATIONS OF Four Basic Factors ror THE THREE GROUPS 


Boys Hieu WADLEIGH De Wirt Ciinton 


Thorn- Thorn- | Elem. Thorn-| Elem. 
Beta Age | dikeB| Beta Age |dikeB| Av. Beta Age |dikeB| Av. 


Briggs Beta. —.2772) .3931 —.0798) .6014) .4451 — .2482] .2873] .1922 


ABO cre acejehs — .2772 — .1225|}— .0798 — .0212|— .1622|}— .2482 — .2922)— .1865 
Thorndike B.| .3931)}—.1225 .6014|— .0212 .8278| .2873|}—.2922 2514 
Elem. Aver- 

BIO eas .4451|— .1622| .3278 — .1922)—.1865} .2514 


Table XIII shows the multiple ratio coefficients when one, 
two, three, and four of the factors are in the combination. The 
accretions to the previous coefficients are also shown. 

We note from Table XIII that the four basic factor combination 
gives for the De Witt Clinton group a coefficient of .7227; for the 
Wadleigh, .6484; and for Boys High, .5639. The coefficients in 
the case of the De Witt Clinton group, as various factors are added, 
run considerably higher than in the case of the Wadleigh. In the 
De Witt group, Age, with a criterion correlation of —.57, makes a 
tremendous contribution. The Boys High correlations run con- 
siderably lower for reasons that have been explained. We have 
selected from Allen’s group those pupils still in school at the end 
of the third semester. By this selection, as seen on page 21, the 


Statistical Treatment 37 


TABLE XIII 


SHow1nG MuurtieLe CoErricrENts ror THREE Groups witH Four Basic 
FAcrors IN THE COMBINATION 


De Wirt 
Boys Hicu WADLEIGH aren aus 
Amount Amount Amount 
’ Added , | Added ' Added 
IC to IC to IC to 
Tic! Tic! ric 
Briggs Beta alone........ .5314 5034 A721 
Briggs Beta, Age......... 5475 | .0161 | .6107 | .1073 | .6614 | .1893 
Briggs Beta, Age, Thorn- 
UIKeR IA AY eee see . 5639 .0164 | .6249 .0142 | .7080 . 0466 
Briggs Beta, Age, Thorn- 
dike B, and Elementary 
PAMTEYADO . Gtncta saree ys . 6484 -0235 | .7227 0147 


criterion correlation of Briggs Beta has fallen from .56 to .53; 
Thorndike B, from .38 to .34. Also, due Jargely to this selection, 
the correlation of Age with the criterion in this group runs con- 
siderably lower. No elementary marks were obtained for this 
group. Had scores in the four basic factors for all of Allen’s 
pupils been secured, the results for this group would no doubt 
approximate those of the other two. 


D 


ADDITION OF OTHER Factors TO THE Four Basic Factor 
CoMBINATION 


It should be clear from the preceding pages that the applica- 
tion of the Toops’ multiple ratio correlation formula makes it pos- 
sible to construct norms at different levels. If we give one test 
or use one factor, we obtain a certain multiple ratio correlation. 
The addition of another test or factor gives a higher correlation, 
and so on. ‘The significance of different correlations will be indi- 
cated in the next chapter. To be practical administratively, the 
amount a test or factor adds must justify the extra effort required. 

It was decided to add the other factors in the experiment to the 
“four basic factor combination.”’ From a practical point of view 
it was not necessary to go through the statistical computation for 
every individual item. For example, the correlations of the twelve 


38 Detailed Factors in Latin Prognosis 


traits with the criterion run close together. Having the contri- 
bution of one to the multiple correlation ratio, we can estimate 
fairly closely the contribution of another. Thus, the foregoing 
data in this experiment made it possible to abbreviate somewhat 
the complete list of items in the following ways: 

1. The elementary school average showed consistently with the 
criterion and in the combination approximately as high a correla- 
tion as any elementary school mark. Being an average, it is more 
reliable than any of them. Hence, elementary average was the 
only item used for the elementary marks. 

2. English and mathematics showed the highest consistent cor- 
relation with the criterion of any of the high school marks. So 
the average of the English and mathematics marks was used as a 
single item from the list of high school marks. The Wadleigh 
group did not have mathematics; so English alone was used. 

3. The correlations of the twelve traits run close together for 
each group. ‘Two items were placed in the combination: (a) Ac- 
curacy. (b) Sum or composite score on all traits except “fre- 
quency of help.” 

4. From the factor, “time spent on study,’ two items were 
selected: (a) Time spent on Latin. (b) Combined time spent on 
other subjects. , 

By the above plan the original list was reduced to 24 items 
exclusive of the “‘four basic factors.”’ Tables XIV and XV, fol- 
lowing, show respectively for the Wadleigh and De Witt Clinton 
groups the following data: 


1. Intercorrelations of the 24 items with each of the four basic 
factors. ; 

2. Multiple ratio coefficients. 

3. Amount each factor adds to the four basic factor combination. 


Tables XIV and XV show that in each of the two groups only 
three items make any significant contributions, when tested with 
the four basic factor combination. These three factors are: 
(English and mathematics), accuracy, sum of traits. They add 
in the case of each group as follows: 


De Witt 

Wadleigh Clinton 
(English and Mathematics)................ 04 .07 
AGCUTECY 0") 0 cps ae See ce eles ee 14 .08 


Sum of Traits Gries ee peter eee Beene .16 .10 


ONOORWNH 


CONDOR Whe 


Re 
rt OO 


12 


1 
te Co 


15 


eT, 
18 
19 
20 
21 
22 
23 
24 


_ 
a 


Statistical Treatment 


TABLE XIV 


39 


SHOWING TESTING oF 24 IreMs witraH “‘ Four Bastc Facror CoMBINATION”’ 


. Briggs Alpha... 


ee: be, eee 


MeL HOYNCIKC Al addeces oe 
Mabmternolation: 1.505 .o< eee 
meiner polavlony 2s. icc coe: 


. Elementary Atte 


. Av. (English & Mathema- 


ndance.. 


HICS) Ge oe tehiae ores 
WPL OCULBOT s/o )no ae 6 sacle 
Pe OUMMIOL LTalts.t tous Saat 


. Minutes of Help 
MAIVEO VICES <taenc eres 


awl se @n6. > reve 


ele 10 bre 6.8 (6 


eep 
. Plan after Graduation.... 


PEP Ia TY TOL. Lilte’. 7, See eek 


. Music Lessons. . 
. Outside Languag 


eee wen ws 


CB rita «210s 


bowWorkitor Parents... 3.0. 
Slime Spent, watin ss... 2 


. Time Spent, Other Subjects 


. Importance of Subject.... 
. Preference for Subject.... 
. Preference for Teacher... 


. Extra-Curricular 


3, bP Oo) 8! ow a 


WADLEIGH GROUP 


INTERCORRELATION 
Briggs Thorn- 
Beta Age dike B 
8990 | —.1108 5829 
6160 | —.0515 .9128 
2155 0637 .0950 
8942 | —.2209 .2451 
6071 | —.5708 .7219 
0950 | —.1691 | —.0295 
0689 | —.0004 .0304 
6367 | —.1329 .6670 
1281 | —.2810 | —.0071 
.1876 | —.2974 0424 
— .0671 | —.1218 | —.1397 
.0548 .0809 | —.0811 
.0774 — .0418 1164 
.0646 | —.2628 .0626 
.0205 | —.0238 | —.0034 
.0416 | —.1942 | —.0504 
.0080 | —.0973 | —.0449 
— .0750 . 2049 .0823 
0687 .1145 . 2266 
— .3106 2101 | —,2865 
—.0876 | —.0225 | —.0369 
— .2993 | —.1965 | —.5116 
3954 | —.0558 | —.6521 
1473 | —.0019 2154 
TABLE XV 


SHOWING TESTING OF 24 IrEMs witH “‘ Four Basic Factor CoMBINATION”’ 


. Briggs Alpha... 


ee NOENGIKGrA] packets cect 
EinterpolabioneL sea\ cr, 5.2cr- 
SInterpolation: 2.3.2.0. .: 


Sb atkey ew eis. at ef 6 (e; © 10) 6\'8\ 161s (6, 0".6 


. Av. (English & Mathe- 


matics) ids +’: 


. Minutes of Help 


iw OL Ov.a at a! 07's 


p AOCULBOY 2. vers ssa ns oe es 
Plt OE. Era tes ahscyseas Ree 


epee, o) ove) eye 


aS Cesare peewee 5 eek one ae 


ep ; 
. Plan after Graduation.... 


S Plan tor [Late 2c ooo oe te oe 


. Music Lessons. . 


ol feA SUP Ae, 0' iw ve: 


. Outside Language....... 
. Work for Parents........ 
Te Lime spent, LAatli~e.2... 


. Time Spent, Other Subjects 


. Importance of Subject... 
. Preference for Subject.... 
. Preference for Teacher... 


. Extra-Curricular 


eee eo eo tie 


De Wirt Cruinton Group 


INTERCORRELATION 

Briggs Thorn- 
Beta Age dike B 
8640 | —.3077 BLS 
2453 | —.3449 .8205 
4041 — .3452 1159 
4412 | —.3215 .1973 
.4401 | —.6603 .6476 
.1815 .0311 | —.1082 
—.0063 | —.0496 | —.1250 
4518 | —.4346 3137 
2833 | —.5172 1923 
2873 | —.4589 1738 

— .1631 .0964 0302 
— .1163 .0740 | —.1276 
.0335 | —.2194 1451 
2350 — .1250 rLLoL 
0899 — .2141 — .0088 
1155 | —.1381 | —.0037 
—.0006 | —.1006 | —.0170 
0276 1442 — .1633 
— .1319 1061 | —.1882 
— .0865 .0934 — .1946 
— .0434 | —.1038 1091 
2453 | —.3968 2277 
2219 — .2401 3741 
0384 .0089 0739 


40 Detailed Factors in Latin Prognosis 


Preference for teacher adds .07 in the case of Wadleigh, but only 
.01 in the case of De Witt Clinton. Preference for subject adds 
.02 and .03, respectively, for the two groups. Movies, and aca- 
demic interest as shown by plan for life work, each adds .02 in the 
case of Wadleigh, but neither factor makes any contribution to De 
Witt Clinton. The contributions of all other factors are insig- 
nificant. 

Inasmuch as (English and mathematics), accuracy, and sum of 
traits do not belong to the purely predictive class of factors, Tables 
XIV and XV verify the fact that, for predictive purposes, the 
four basic factor combination is in all probability the best com- 
bination. 

Sum of traits, which includes accuracy, makes a greater contri- 
bution than accuracy alone. Both accuracy and sum of traits 
make a greater respective contribution than (English and mathe- 
matics). Hence, it was decided to retain sum of traits in com- 
bination with the four basic factors and to add (English and 
mathematics). With five factors in the combination: Briggs 
Beta, Age, Thorndike B, Elementary Average, Sum of Traits, 
the multiple ratio coefficients are .8049 and .8239, respectively, 
for Wadleigh and De Witt Clinton. Adding English to Wadleigh 
and (English and mathematics) to De Witt Clinton, the coeffi- 
cients become .8241 and .8400, respectively. These two multiple 
ratio coefficients, with six factors in the combination: Briggs Beta, 
Age, Thorndike B, Elementary Average, Sum of Traits, (English 
and mathematics), are the highest accumulated correlation co- 
efficients obtained in this experiment. They were obtained by 
sifting the data of the sixty items of the experiment for elements 
in common or indicative of success in first year Latin, as measured 
by the Latin criterion tests used in the experiment. As stated 
previously, four of these items belong to the purely predictive 
type: Briggs Beta, Age, Thorndike B, Elementary Average. The 
fifth factor, Sum of Traits, is “‘affective’’; the sixth, (English and 
mathematics), is predictive in the event that first year Latin be 
not commenced until the second semester. Otherwise, it is affec- 
tive or relational. 

It will be recalled that, in the case of the Boys High group, ele- 
mentary average and sum of traits are lacking. Thus, we have 
for this group only four of the six factors selected above, and only 
three of the four basic factor combination. An examination of 


Statistical Treatment 41 


the low criterion correlations of many items of this group shows a 
close correspondence with the criterion correlations of the other 
two groups. Reference to Tables XIV and XV shows that such 
low criterion correlations can make no significant contribution, 
and that the testing of them is a waste of time. It was decided, 
therefore, to test the following eight items with three basic factors 
in the combination. ‘The results are shown in Table XVI. 


TABLE XVI 
SHOWING TEsTING OF 8 ITEMS witH THREE Basic Factors IN THE COMBINATION 


Boys Hicu Group 


INTERCORRELATION Amount 
Added 
. ey) to 

Briggs Ape Thorn- foal 
Beta dike B 5639 
High School Attendance.....| —.0515 | —.0274 | —.0577 | .5639 . 0000 

English and Mathematics... . .5037 | —.2503 4347 | .6558* | .0919* 
Preference for Teacher...... — .0448 .0615 | —.0237 | .5786 .0147 
Binsrnciice A Se) ose ees .9752 | —.1320 8072 | .5669 0030 
Interpolation’) © o.can. « oers .3194 | —.1932 3070 | .5667 0028 
PreeETOaONiee-. tek ote .1994 | —.1887 .1710 | .5640 .0001 
Briggs Alpha............... 8203 | —.2255 3987 | .5640 | .0001 
LO io eae te MER sui Si ee gn ni 4848 | —.2143 5809 5652 0013 


(English and mathematics) gives a correlation coefficient of 
.6558 when added to the combination. It contributes .09, prac- 
tically the same as in the case of the other two groups. Preference 
for teacher adds .01. The other additions are even more trivial. 
For this group, in which only four of the six factors used in the 
other two groups are available, the highest correlation coefficient 
obtained is .6558. 


CHAPTER V 
PRACTICAL IMPLICATIONS 


In this experiment, multiple ratio correlation coefficients have 
been secured for the following combinations: 


1. The four basic factor combination: Briggs Beta, Age, 
Thorndike B, Elementary Average. 

2. The six factor combination: Briggs Beta, Age, Thorndike B, 
Elementary Average, Sum of Traits, Average (English 
and Mathematics). 

3. The Allen Prognosis Battery: Briggs Analogies Tests, Alpha 
and Beta; Thorndike Word Knowledge Tests A and B; 
Rogers Interpolation Tests 1 and 2. 

4. The Allen Prognosis Battery plus Age and Elementary 
Average.! 

5. The seven factor combination for the Wadleigh group: 
Briggs Beta; Age; Thorndike B; Sewing and Cooking; 
Physical Training; Penmanship, Music, and Drawing; 
General Estimate. 


TABLE XVII 
SHowING MuttieLe Ratio CoErricieENts oF ALL COMBINATIONS FOR 
THREE GROUPS 


Boys High | Wadleigh | De Witt Clinton 


. Four Basic Factor Combination. . . . 56394 . 6484 7227 


1 
2, Six Factor Combination......... . 6558» 8241 . 8400 
8. Allen Prognosis Battery.......... . 5634 . 6672 
4, Allen Prognosis Battery plus Age 
and Elementary Average....... . 6582 TATA 
5. Seven Factor Combination for the 
Wadleigh Group. ............- . 6903 
8 Hlementary average lacking. b Elementary average and sum of traits lacking. 


Table XVII shows the correlation coefficients obtained for these 
combinations with the three groups. Only three factors of the 
four factor combination are present for the Boys High group: 

1 Age alone raises Allen Battery to .6419 and .7324 for Wadleigh and De Witt 
Clinton, respectively. 

42 


Practical Implications 43 


Briggs Beta, Age, Thorndike B. Only four factors of the six 
factor combination are present for the same group: Briggs Beta; 
Age; Thorndike B; Average of English and Mathematics. 

In the practical interpretation of the above coefficients, two 
questions suggest themselves: 

First, in terms of the data of this experiment, what do the 
correlation coefficients for these five combinations represent? 


1. The first combination consists of four predictive factors, 
that is, factors for which objective data may be secured 
before the pupil begins the study of Latin. 

2. The second combination consists of four predictive factors, 
a fifth which is “‘affective,” and a sixth which is predictive 
in the event that first year Latin be not commenced until 
the second semester. This combination shows the achieve 
ment of pupils of a given age and capacity who in the 
judgment of the individual teacher possess certain traits 
of character and of industry. 

3. The third combination is predictive and consists of six ob- 
jective factors. 

4. The fourth combination consists of eight objective factors, 
all of which are predictive. 

5. The fifth combination consists of three objective factors and 
four of a less objective nature. 


The second question which suggests itself is, ““What do these 
correlations mean? How are they to be interpreted?” 

No one can tell with absolute accuracy just what a coefficient 
of correlation means. Professor Edward L. Thorndike in Tables 
XVIII and XIX, which are used here with his permission, has 
given the best approximation. Table X VIII shows when the cor- 
relation of any factor or combination is .60, that 39.2 per cent 
of the first tenth will be placed in the first tenth, 20.4 per cent of 
the second tenth will be placed in the second tenth, 13.7 per cent 
of the third tenth in the third tenth, andso on: Table XIX shows 
the distribution of successive tenths of the group when the correla- 
tion is .80. In this case, 56.2 per cent of the first tenth will be 
placed in the first tenth, 23.1 per cent of the second tenth in the 
second tenth, and so on. 

Of all the correlations in Table XVII, Figures 1 to 4, with the 
discussion which follows, illustrate the significance of four specific 


Ad Detailed Factors in Latin Prognosis 


correlations. They range from .5634 to .84. Figure 1 shows for 
the Wadleigh group the distribution of pupils on the Allen Prognosis 
Battery and the Latin criterion, correlation .5634. Figure 2 shows 
for the Wadleigh group the distribution of pupils on the six factor 
combination and the Latin criterion, correlation .8241. Figure 3 
shows the distribution of pupils for De Witt Clinton on the Allen 
Battery and the Latin criterion, correlation .6672. Figure 4 shows 
the distribution of pupils for the De Witt Clinton group on the six 
factor combination and the Latin criterion, correlation .84. The 
composite score of pupils in each of the above combinations was 
found by the method explained on page 16. The constant quo- 
tients were obtained by dividing the true weight of a factor by its 
sigma. 

By a careful examination of Figures 1 to 4 in relation to pupil 
achievement, as measured by the teacher’s mark at the end of the 
semester, the following facts are revealed. 


A 


WaDLEIGH GROUP 


On Figs. 1-4 the circles indicate the pupils who failed Latin. 
Of the 80 pupils, 11 or 13.75 per cent failed Latin for the semes- 
ter, the passing mark being 60 per cent. Although the criterion 
was not used as final examination, 100 per cent of the failures were 
below the average on the criterion; 81.8 per cent were below the 
average on the Allen Battery. If we choose some arbitrary score, 
such as 8 on Figure 1, we find that 54.5 per cent of the failures and 
four pupils who passed are below 8. The average mark of these 
four is 81.25 per cent; 63.6 per cent of failures and nine who passed 
fall below 9 on the Allen Battery. The average mark of those who 
passed was 78 per cent. 

On the six factor combination (Figure 2), 18.2 per cent of the 
failures and no one who passed fall below 3; 27.3 per cent of the 
failures and no one who passed fall below 4; 72.7 per cent of the” 
failures fall below 5, that is, in the lowest decile, with no one who 
passed included. 

B 


Dre Wirt CLinton GRouP 


In the case of the Allen Battery, 20 per cent of the failures and 
seven pupils passed by the faculty are below 8. The average 


Practical Implications AD 


¢ EEE 
gE tet totter te 
eee a ae / 

UU SES 2a Da a DL TR ee 
TT SE RS | Wa 
EECA tet PE 
_ 0 We \\ a | 
cy calcd al ES Fa DD tre FH 
Q 
ee oer ee ye rien nr anlar | 
fo SUES ed ea | 
ON TTS a Bad a oa Ts | Ve 

+ NCS EATS ed (a 

2c GT EH ST A | 

3 a} } Hy 

sp a ee oe We ik on | ea a eS | ie da 

24S NT aR SB 2 P| ee 

0 a Fe a ONS | a8 P| 

° 1 ed 3 + 5 10 it [a tS 4 tS) IS 17 


ME AN-IL-8 
LATIN CRIT & RibO'N: 


Figure 1. SHowi1na DistrRiBuTIon or WADLEIGH GROUP ON ALLEN PROGNOSIS 
BATTERY AND THE LATIN CRITERION 


ey SS 2 TE Ba ee Ee | 
LA Ee oe 
/ 


Raa ESR 
gepzeeeenoad usnee 
ial i MEAN 
2 SS ae ee 

ea a | ial 


SIX FACTOR COMBINATION. 


| Sn Be 
Seas ek Sat) Sep NN Rh pe be eB 
eee es et eG en Bo) SiO th eS. 1A CIS. 16 OF 
MEAN-I1.& 
LATIN CRITERION. 


Figure 2. SHowrne DISTRIBUTION OF WADLEIGH GROUP ON THE “Srx Factor 
CoMBINATION”’? AND THE LATIN CRITERION 


46 Detailed Factors in Latin Prognosis 


eee eo 
16 

PREM cn ke = 
RM RMRIGRSILEC Doicicnen 
TRIG mses ES 


may, 


S 


Ee, 
ars rai te a aie 
is mets a Po far ee 
yA Se On| _7 Wi Mean. 
ee ah o Ml oa i 
z § oi Pe et eal 
aS ROR Me Re PEE Sie a is BS) 
cA oe Aa 
Rise ae a ee fata i a 
xf ee Be ek Nee Remen re 
oe 


fa DAB es c= 

pe I le Set ea aa 

2 AO SIL Ie SO NE TS oe 
MEAN-1.8& 

LATIN CRITERION. 


Figure 3. SHowi1ne DIstrRiBsuTion or DE Witt Ciinton Groupe on ALLEN 
Prognosis BATTERY AND THE LATIN CRITERION 


Son ea SF Ost = ats Ns So eas 


MEAN-II-8 
LATIN CRITERION. 


ee 
Figure 4. Snowrne Distrrsution or Dr Wirt Ciinton Group ON THE “SIX 
Factor CoMBINATION” AND THE LATIN CRITERION 


Practical Implications AT 


mark of these seven pupils is 75 per cent. Forty per cent of the 
failures and fourteen who passed are below 9. The average of 
these nine is 74.6 per cent. 

In the case of the six factor combination, 40 per cent of the 
failures and one pupil who passed are below 3. The mark of this 
one pupil is 65 per cent. Ninety per cent of the failures and six 
pupils who passed are below 4. The average of these four pupils 
is 66.66 per cent with no one above 75 per cent. One hundred 
per cent of the failures and ten who passed are below 5, that is, 
in the lowest quartile. These ten have an average mark of 69 
per cent with no one above 75 per cent. The lowest decile in- 
cludes 60 per cent of the failures with only two who passed. The 
average mark of these two is 70 per cent. 

The preceding analysis shows that the six factor combination is 
very much more effective than the Allen Prognosis Battery in 
selecting pupils on the basis of achievement. While this is true, 
it must be recognized that the six factor combination contains 
two factors not actually obtainable until the pupil is in high 
school: Sum of Traits, English and Mathematics. The Allen 
Prognosis Battery, with Age and Elementary Average also in the 
combination, giving correlations of .6582 for Wadleigh and .7474 
for De Witt Clinton, would probably show a selective efficiency 
midway between the Allen Battery and the six factor combina- 
tion. The relative selective ability of the various correlation 
coefficients, given in Table XVII, may be approximately obtained 
from Tables XVIII and XIX and the foregoing illustrations. 


TABLE XVIII 


DISTRIBUTION OF AVERAGE OF SUCCESSIVE TENTHS OF THE GROUP 
WHEN r=.60 (APPROXIMATE) 


tat tenth... hsv. 2 “8 eS 29 4.6 6.6 9.7 | 18.7 | 20.4 | 39.2 
2nd tenth....... Hv, 2.6 4.3 6.0 8.2 | 10.38),-18.0 | 15.6 | 18.7 | 20.4 
Srd tenth. ...:... 1 os: 4.3 6.4 res LO de | ee else deen ah oot mel ede Com ee One Cree ime eden dy 
4th tenth....... 2.9 6.0 8.2 9.8 | 11.4 | 12.4 | 13.2 | 13.5 | 13.0 OE 
Sth tenth....... 4.6 SeZe MLO gl tale ZEON 2 Os bares etl iene 6.6 
6th tenth....... CEOs On Se UIT L2eA eos Qala Ose 8.2 4.6 
PUM CENED yes ac OA ele Oe ls OUP loe2e lta Aa Ve. 4 9.8 8.2 6.0 2.9 
Sthetenth sa... « LS Vim L Oc Omi lei srl arom et legal LOee 8.2 6.4 4.3 1.8 
Oth tenth. ...... 20.4 | 18.7 | 15.6 | 13.0 | 10.3 8.2 6.0 4.3 2.6 A 
10th tenth....... 39.2 | 20.4 | 13.7 9:7 6.6 4.6 Zine 1.8 3, .2 


This table was computed by Professor E. L. Thorndike and is used here with his permission. 


Detailed Factors in Latin Prognosis 


48 


TABLE XIX 
DISTRIBUTION OF ARRAYS IN SUCCESSIVE TENTHS OF THE GROUP 


WHEN r=.80 


9th 8th 7th 6th 5th 4th 3rd 2nd Ist 


10th 


Areas tHoOnte 


Pr yl ia ee ee eee a 


LN COIS PLO NL N 
aes 


OIADOWOOVOr 


NO 09190 OLIDN OD Hes 
ronan ian ian ie 


MFOOWMMOANINS 
ra HOD N19 O19 OD CON 
Soon len fan fan a 


SHIDO NO DOr H 
O21 DAO & Dh 0910 
anne 


MODOOANRHOr 
ANMOMM~-OOM 
mrAANnd 


OOH OO INO rs 
MPN HOM OO OD 
MANNS 


AHR OMHHN 


Ist tenth 
2nd tenth 
3rd tenth 
4th tenth 
5th tenth 
6th tenth 
7th tenth 
8th tenth 
9th tenth 
10th tenth. 


CHAPTER VI 


SUMMARIZED CONCLUSIONS 


I. The Briggs Analogies Tests, of all factors used in this experi- 
ment, are the best single objective measures for predicting achieve- 
ment in first year Latin. Either Alpha or Beta has a consistent 
average correlation of .50 with the Latin criterion tests given at 
the end of the semester. 

II. The Allen Battery of prognosis tests: Briggs Analogies 
Alpha and Beta; Thorndike Test of Word Knowledge A and B; 
Rogers Interpolation 1 and 2, predict Latin achievement for dif- 
ferent groups, with an average correlation of .60 or above. Allen 
obtained a correlation of .588 for 364 pupils in the Boys High 
School, Brooklyn. The writer, with the Allen Battery, secured 
a correlation of .563 for 80 girls at Wadleigh High School, and a 
correlation of .667 for 103 boys at De Witt Clinton High School. 
By the addition of age and the average of all marks for the last 
year of the elementary school, to the Allen Battery combination, 
the correlations were raised to .658 and .747 for Wadleigh and De 
Witt Clinton, respectively. Allen’s tests require 70 minutes of 
time, and the last two factors come from the school record. 

III. The four predictive factors: Briggs Beta, Age, Thorn- 
dike B, Elementary Average, give in combination a correlation 
of .648 for Wadleigh, and .723 for De Witt Clinton. To secure 
data for the first and third factors requires 26 minutes of testing. 
The other two are items of ordinary school record. When the 
Latin teacher’s judgment of pupils on eleven character and indus- 
try traits is added, as a fifth factor, to the above combination, the 
correlations become .805 and .824. To obtain this factor requires 
approximately an hour of the teacher’s time. High school Eng- 
lish added as a sixth factor to the Wadleigh group raises the corre- 
lation to .824. An average of high school English and mathe- 
matics added to the De Witt Clinton group raises the correlation 
to .840. The last factor is also an item of school record. 

IV. The following seven predictive factors: Briggs Beta; Age; 
Thorndike B; Sewing and Cooking; Physical Training; Penman- 
ship, Music, and Drawing; General Estimate; in combination, gave 


49 


50 Detailed Factors in Latin Prognosis 


for the Wadleigh group a correlation of .690. ‘The marks in this 
combination are for the last year of the elementary school. The 
factors for this combination were selected solely on the basis of 
how much they would add, regardless of their objectivity. 

V. The highest correlation coefficients for the Boys High group 
are below the highest for Wadleigh and De Witt Clinton. Two 
reasons for this are evident. First, two factors, Elementary Av- 
erage and Sum of Traits, are lacking for this group. Second, 
Allen’s original correlations were greatly reduced by the selection 
of 215 of his original 364 pupils still in school at the end of the 
third semester. The following four factors in combination: 
Briggs Beta, Age, Thorndike B, Average of English and Mathe- 
matics, give for this group a correlation of .656. 


APPENDIX ! 


Forms of the same Latin criterion tests were given to the Wadleigh 
and De Witt Clinton groups at the end of the second semester. 
There were 60 pupils still in school and available at Wadleigh, 67 
at De Witt Clmton. Tables XX and XXI show the respective 
results for the two groups, using the data of the six factor com- 
bination that were secured the first semester. This combination 
consists of: Briggs Beta, Age, Thorndike B, Elementary Average, 
Sum of Traits, English and Mathematics (English alone in case 
of Wadleigh). 

Tables XX and XXI show that the correlations of the six factor 


TABLE XX 


SHOWING THE Six Factor CoMBINATION FOR THE SECOND SEMESTER 
WaADLEIGH GROUP 


INTERCORRELATION 

é Corre- | Amount 
CS —— | lation to Added 

terion Combi- tH 

Grol teres Thorn-| Elem. | Sum nation| ,, 

Age dike | Aver- of Eng- (r-/) Ic 

Beta B age | Traits] lish Ic 
Briggs Beta... . 2336 . .0854| .6870]} .3820|/—.0082] .4885] .2336 
(A PORE hace ee —.0514] .0854 — .0003] — .1296} —.0303] —.1028] .2443 .0107 
Thorndike B.. 3063] .6870} —.0003 .38550) —.0551] .6845) .3105 .0662 
Elem. Average.| .3983] .3820}—.1296] .3550 .2669| .2262) .4327 ml 22 
Sum of Traits. .3603} — .0082} —.0303] —.0551} .2669 Salalah an teye .0860 
DIEING ivan ae .38460} .4885)—.1028} .6845} .2262) .1157 .5400 .0213 
TABLE XXI 


SHOWING THE Srx Factor COMBINATION FOR THE SECOND SEMESTER 
De Wirt Ciinton Group 


INTERCORRELATION 
Corre- | Amount 
Cri- - ete Added 
terion ombi- to 
4 Thorn- | Elem. Sum Eng- . 
(xc) | Briges| Age | dike | Aver- | of |lish and Sa. hee 
Beta B age | Traits | Math. Ic 
Briggs Beta... 4404 — .2446 2559 -1300D .1745 .4531] .4404 
Te en a — .5380| —.2446 — . 2690] — .0806] —.3772| —.3899| .6252 . 1848 
Thorndike B.. 2851 2559] — .2690 2921 0074 SPE ETAL worn Oi .0055 
Elem, Average. 1425 . 1355} — .0806 2921 .1895| .4735) .6320 .0013 
Sum of Traits. 5291 .1745| — .3772 .0074 . 1895 .4515| .7106 .0786 
English and 
Wath: 2565 .6115] .4531] —.3899 DESY .4735}| .4515 . 7443 .0337 


1 Tables showing complete data for this study are on file in the Teachers College 
Library. 


51 


52 Detailed Factors in Latin Prognosis 


combination for the second semester are .54 and .7443, respec- 
tively, for the Wadleigh and the De Witt Clinton groups. These 
are considerably lower than for the first semester. Selection has 
no doubt made the group more homogeneous, as proved to be true 
when Dr. Allen’s original group of 364 was reduced to 215. Inthe 
second place, the criterion tests in their present form seem designed 
primarily for the first rather than the second semester’s work. To 
be equally satisfactory for the second, they should be revamped 
to measure the specific material studied during the second semes- 
ter. This was not practicable in the present experiment. It 
would involve the development of a new set of tests, destroy 
comparability, and complicate the main problem. To devise a 
new set of tests, based on the same technique but designed pri- 
marily for material of the second semester, is suggestive for future 
experiment. It would make possible a more thorough testing of 
the combinations developed in this study. 


00 


